diff --git a/.github/workflows/R-CMD-check.yaml b/.github/workflows/R-CMD-check.yaml
index 14159b7..d46a617 100644
--- a/.github/workflows/R-CMD-check.yaml
+++ b/.github/workflows/R-CMD-check.yaml
@@ -6,7 +6,9 @@ on:
   pull_request:
     branches: [main, master]
 
-name: R-CMD-check
+name: R-CMD-check.yaml
+
+permissions: read-all
 
 jobs:
   R-CMD-check:
diff --git a/.github/workflows/R-CMD-historic-R-check.yaml b/.github/workflows/R-CMD-historic-R-check.yaml
deleted file mode 100644
index 58be7da..0000000
--- a/.github/workflows/R-CMD-historic-R-check.yaml
+++ /dev/null
@@ -1,46 +0,0 @@
-# Workflow derived from https://github.com/r-lib/actions/tree/v2/examples
-# Need help debugging build failures? Start at https://github.com/r-lib/actions#where-to-find-help
-on:
-  push:
-    branches: [main, master]
-  pull_request:
-    branches: [main, master]
-
-name: R-CMD-historic-R-check
-
-jobs:
-  R-CMD-check:
-    runs-on: ${{ matrix.config.os }}
-
-    name: ${{ matrix.config.os }} (${{ matrix.config.r }})
-
-    strategy:
-      fail-fast: false
-      matrix:
-        config:
-          - {os: ubuntu-latest,   r: 'oldrel-2'}
-          - {os: ubuntu-latest,   r: 'oldrel-3'}
-
-    env:
-      GITHUB_PAT: ${{ secrets.GITHUB_TOKEN }}
-      R_KEEP_PKG_SOURCE: yes
-
-    steps:
-      - uses: actions/checkout@v3
-
-      - uses: r-lib/actions/setup-pandoc@v2
-
-      - uses: r-lib/actions/setup-r@v2
-        with:
-          r-version: ${{ matrix.config.r }}
-          http-user-agent: ${{ matrix.config.http-user-agent }}
-          use-public-rspm: true
-
-      - uses: r-lib/actions/setup-r-dependencies@v2
-        with:
-          extra-packages: any::rcmdcheck
-          needs: check
-
-      - uses: r-lib/actions/check-r-package@v2
-        with:
-          upload-snapshots: true
diff --git a/.github/workflows/lint.yaml b/.github/workflows/lint.yaml
index f60d047..018b8db 100644
--- a/.github/workflows/lint.yaml
+++ b/.github/workflows/lint.yaml
@@ -6,7 +6,9 @@ on:
   pull_request:
     branches: [main, master]
 
-name: lint
+name: lint.yaml
+
+permissions: read-all
 
 jobs:
   lint:
diff --git a/.github/workflows/pkgdown.yaml b/.github/workflows/pkgdown.yaml
index a7276e8..4bbce75 100644
--- a/.github/workflows/pkgdown.yaml
+++ b/.github/workflows/pkgdown.yaml
@@ -9,7 +9,9 @@ on:
     types: [published]
   workflow_dispatch:
 
-name: pkgdown
+name: pkgdown.yaml
+
+permissions: read-all
 
 jobs:
   pkgdown:
diff --git a/.github/workflows/pr-commands.yaml b/.github/workflows/pr-commands.yaml
deleted file mode 100644
index eea58c5..0000000
--- a/.github/workflows/pr-commands.yaml
+++ /dev/null
@@ -1,79 +0,0 @@
-# Workflow derived from https://github.com/r-lib/actions/tree/v2/examples
-# Need help debugging build failures? Start at https://github.com/r-lib/actions#where-to-find-help
-on:
-  issue_comment:
-    types: [created]
-
-name: Commands
-
-jobs:
-  document:
-    if: ${{ github.event.issue.pull_request && (github.event.comment.author_association == 'MEMBER' || github.event.comment.author_association == 'OWNER') && startsWith(github.event.comment.body, '/document') }}
-    name: document
-    runs-on: ubuntu-latest
-    env:
-      GITHUB_PAT: ${{ secrets.GITHUB_TOKEN }}
-    steps:
-      - uses: actions/checkout@v4
-
-      - uses: r-lib/actions/pr-fetch@v2
-        with:
-          repo-token: ${{ secrets.GITHUB_TOKEN }}
-
-      - uses: r-lib/actions/setup-r@v2
-        with:
-          use-public-rspm: true
-
-      - uses: r-lib/actions/setup-r-dependencies@v2
-        with:
-          extra-packages: any::roxygen2
-          needs: pr-document
-
-      - name: Document
-        run: roxygen2::roxygenise()
-        shell: Rscript {0}
-
-      - name: commit
-        run: |
-          git config --local user.name "$GITHUB_ACTOR"
-          git config --local user.email "$GITHUB_ACTOR@users.noreply.github.com"
-          git add man/\* NAMESPACE
-          git commit -m 'Document'
-
-      - uses: r-lib/actions/pr-push@v2
-        with:
-          repo-token: ${{ secrets.GITHUB_TOKEN }}
-
-  style:
-    if: ${{ github.event.issue.pull_request && (github.event.comment.author_association == 'MEMBER' || github.event.comment.author_association == 'OWNER') && startsWith(github.event.comment.body, '/style') }}
-    name: style
-    runs-on: ubuntu-latest
-    env:
-      GITHUB_PAT: ${{ secrets.GITHUB_TOKEN }}
-    steps:
-      - uses: actions/checkout@v4
-
-      - uses: r-lib/actions/pr-fetch@v2
-        with:
-          repo-token: ${{ secrets.GITHUB_TOKEN }}
-
-      - uses: r-lib/actions/setup-r@v2
-
-      - name: Install dependencies
-        run: install.packages("styler")
-        shell: Rscript {0}
-
-      - name: Style
-        run: styler::style_pkg()
-        shell: Rscript {0}
-
-      - name: commit
-        run: |
-          git config --local user.name "$GITHUB_ACTOR"
-          git config --local user.email "$GITHUB_ACTOR@users.noreply.github.com"
-          git add \*.R
-          git commit -m 'Style'
-
-      - uses: r-lib/actions/pr-push@v2
-        with:
-          repo-token: ${{ secrets.GITHUB_TOKEN }}
diff --git a/.github/workflows/recheck.yml b/.github/workflows/recheck.yml
new file mode 100644
index 0000000..323d2ad
--- /dev/null
+++ b/.github/workflows/recheck.yml
@@ -0,0 +1,18 @@
+on:
+  workflow_dispatch:
+    inputs:
+      which:
+        type: choice
+        description: Which dependents to check
+        options:
+        - strong
+        - most
+
+name: Reverse dependency check
+
+jobs:
+  revdep_check:
+    name: Reverse check ${{ inputs.which }} dependents
+    uses: r-devel/recheck/.github/workflows/recheck.yml@v1
+    with:
+      which: ${{ inputs.which }}
diff --git a/.github/workflows/test-coverage.yaml b/.github/workflows/test-coverage.yaml
index 21b8a93..9882260 100644
--- a/.github/workflows/test-coverage.yaml
+++ b/.github/workflows/test-coverage.yaml
@@ -6,7 +6,9 @@ on:
   pull_request:
     branches: [main, master]
 
-name: test-coverage
+name: test-coverage.yaml
+
+permissions: read-all
 
 jobs:
   test-coverage:
@@ -23,18 +25,27 @@ jobs:
 
       - uses: r-lib/actions/setup-r-dependencies@v2
         with:
-          extra-packages: any::covr
+          extra-packages: any::covr, any::xml2
           needs: coverage
 
       - name: Test coverage
         run: |
-          covr::codecov(
+          cov <- covr::package_coverage(
             quiet = FALSE,
             clean = FALSE,
             install_path = file.path(normalizePath(Sys.getenv("RUNNER_TEMP"), winslash = "/"), "package")
           )
+          covr::to_cobertura(cov)
         shell: Rscript {0}
 
+      - uses: codecov/codecov-action@v4
+        with:
+          fail_ci_if_error: ${{ github.event_name != 'pull_request' && true || false }}
+          file: ./cobertura.xml
+          plugin: noop
+          disable_search: true
+          token: ${{ secrets.CODECOV_TOKEN }}
+
       - name: Show testthat output
         if: always()
         run: |
diff --git a/DESCRIPTION b/DESCRIPTION
index 9199f2a..d7c9075 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -41,7 +41,7 @@ URL: https://larmarange.github.io/labelled/, https://github.com/larmarange/label
 BugReports: https://github.com/larmarange/labelled/issues
 VignetteBuilder: knitr
 LazyData: true
-RoxygenNote: 7.3.1
+RoxygenNote: 7.3.2
 Roxygen: list(markdown = TRUE)
 RdMacros: lifecycle
 Language: en-US
diff --git a/NEWS.md b/NEWS.md
index b47a31f..1972915 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,5 +1,11 @@
 # labelled (development version)
 
+**New features**
+
+* in `update_variable_labels_with()`, it is now possible to access the variable
+  name inside `.fn` by using `names()` (#163)
+* `var_label()` gets new options `"na"` and `"empty"` for `null_action`
+
 # labelled 2.13.0
 
 **New features**
diff --git a/R/update_with.R b/R/update_with.R
index 1d0739c..ef0bd02 100644
--- a/R/update_with.R
+++ b/R/update_with.R
@@ -4,6 +4,11 @@
 #' selected `.cols`.
 #' @param .cols Columns to update; defaults to all columns. Use tidy selection.
 #' @param ... additional arguments passed onto `.fn`.
+#' @details
+#' For `update_variable_labels_with()`, it is possible to access the name of
+#' the variable inside `.fn` by using `names()`, i.e. `.fn` receive a named
+#' character vector (see example). `.fn` can return `as.character(NA)` to
+#' remove a variable label.
 #' @examples
 #' df <- iris %>%
 #'   set_variable_labels(
@@ -18,6 +23,12 @@
 #' df %>%
 #'   update_variable_labels_with(toupper) %>%
 #'   look_for()
+#'
+#' # accessing variable names with names()
+#' df %>%
+#'   update_variable_labels_with(function(x){tolower(names(x))}) %>%
+#'   look_for()
+#'
 #' df %>%
 #'   update_variable_labels_with(toupper, .cols = dplyr::starts_with("S")) %>%
 #'   look_for()
@@ -40,9 +51,19 @@ update_variable_labels_with.data.frame <- function(.data,
     .data,
     allow_rename = FALSE
   )
-  vl <- var_label(.data)
+  vl <- var_label(.data, null_action = "na")
   vl <- vl[names(cols)]
+
+  vl <- mapply(
+    function(variable, label) {
+      setNames(label, variable)
+    },
+    names(vl),
+    vl,
+    SIMPLIFY = FALSE
+  )
   vl <- lapply(vl, .fn, ...)
+  vl <- lapply(vl, unname)
   var_label(.data) <- vl
   .data
 }
diff --git a/R/var_label.R b/R/var_label.R
index d598dd0..9afd6be 100644
--- a/R/var_label.R
+++ b/R/var_label.R
@@ -7,7 +7,8 @@
 #' @param unlist for data frames, return a named vector instead of a list
 #' @param null_action for data frames, by default `NULL` will be returned for
 #' columns with no variable label. Use `"fill"` to populate with the column name
-#' instead, or `"skip"` to remove such values from the returned list.
+#' instead, `"skip"` to remove such values from the returned list, `"na"` to
+#' populate with `NA` or `"empty"` to populate with an empty string (`""`).
 #' @param recurse if `TRUE`, will apply `var_label()` on packed columns
 #' (see [tidyr::pack()]) to return the variable labels of each sub-column;
 #' otherwise, the label of the group of columns will be returned.
@@ -70,7 +71,8 @@ var_label.default <- function(x, ...) {
 #' @export
 var_label.data.frame <- function(x,
                                  unlist = FALSE,
-                                 null_action = c("keep", "fill", "skip"),
+                                 null_action =
+                                   c("keep", "fill", "skip", "na", "empty"),
                                  recurse = FALSE,
                                  ...) {
   if (recurse) {
@@ -98,6 +100,24 @@ var_label.data.frame <- function(x,
     )
   }
 
+  if (null_action == "empty") {
+    r <- lapply(
+      r,
+      function(x) {
+        if (is.null(x)) "" else x
+      }
+    )
+  }
+
+  if (null_action == "na") {
+    r <- lapply(
+      r,
+      function(x) {
+        if (is.null(x)) as.character(NA) else x
+      }
+    )
+  }
+
   if (null_action == "skip") {
     r <- r[!sapply(r, is.null)]
   }
diff --git a/README.md b/README.md
index 6371718..bc7e85c 100644
--- a/README.md
+++ b/README.md
@@ -11,7 +11,7 @@ stable](https://img.shields.io/badge/lifecycle-stable-brightgreen.svg)](https://
 [![CRAN\_Status\_Badge](https://www.r-pkg.org/badges/version/labelled)](https://cran.r-project.org/package=labelled)
 [![Downloads](https://cranlogs.r-pkg.org/badges/labelled)](https://cran.r-project.org/package=labelled)
 [![DOI](https://www.zenodo.org/badge/38772078.svg)](https://zenodo.org/badge/latestdoi/38772078)
-[![Codecov test coverage](https://codecov.io/gh/larmarange/labelled/branch/main/graph/badge.svg)](https://app.codecov.io/gh/larmarange/labelled?branch=main)
+[![Codecov test coverage](https://codecov.io/gh/larmarange/labelled/graph/badge.svg)](https://app.codecov.io/gh/larmarange/labelled)
 <!-- [![Rdoc](https://www.rdocumentation.org/badges/version/labelled)](https://www.rdocumentation.org/packages/labelled) -->
 <!-- badges: end -->
 
diff --git a/man/update_variable_labels_with.Rd b/man/update_variable_labels_with.Rd
index d2f699b..6f07018 100644
--- a/man/update_variable_labels_with.Rd
+++ b/man/update_variable_labels_with.Rd
@@ -22,6 +22,12 @@ selected \code{.cols}.}
 \description{
 Update variable/value labels with a function
 }
+\details{
+For \code{update_variable_labels_with()}, it is possible to access the name of
+the variable inside \code{.fn} by using \code{names()}, i.e. \code{.fn} receive a named
+character vector (see example). \code{.fn} can return \code{as.character(NA)} to
+remove a variable label.
+}
 \examples{
 df <- iris \%>\%
   set_variable_labels(
@@ -36,6 +42,12 @@ df \%>\% look_for()
 df \%>\%
   update_variable_labels_with(toupper) \%>\%
   look_for()
+
+# accessing variable names with names()
+df \%>\%
+  update_variable_labels_with(function(x){tolower(names(x))}) \%>\%
+  look_for()
+
 df \%>\%
   update_variable_labels_with(toupper, .cols = dplyr::starts_with("S")) \%>\%
   look_for()
diff --git a/man/var_label.Rd b/man/var_label.Rd
index cd6bb25..2e40f50 100644
--- a/man/var_label.Rd
+++ b/man/var_label.Rd
@@ -17,7 +17,7 @@ var_label(x, ...)
 \method{var_label}{data.frame}(
   x,
   unlist = FALSE,
-  null_action = c("keep", "fill", "skip"),
+  null_action = c("keep", "fill", "skip", "na", "empty"),
   recurse = FALSE,
   ...
 )
@@ -45,7 +45,8 @@ label_attribute(x) <- value
 
 \item{null_action}{for data frames, by default \code{NULL} will be returned for
 columns with no variable label. Use \code{"fill"} to populate with the column name
-instead, or \code{"skip"} to remove such values from the returned list.}
+instead, \code{"skip"} to remove such values from the returned list, \code{"na"} to
+populate with \code{NA} or \code{"empty"} to populate with an empty string (\code{""}).}
 
 \item{recurse}{if \code{TRUE}, will apply \code{var_label()} on packed columns
 (see \code{\link[tidyr:pack]{tidyr::pack()}}) to return the variable labels of each sub-column;
diff --git a/tests/testthat/test-labelled.r b/tests/testthat/test-labelled.r
index c1ca879..77bdc6d 100644
--- a/tests/testthat/test-labelled.r
+++ b/tests/testthat/test-labelled.r
@@ -1200,6 +1200,26 @@ test_that("null_action in var_label() works as expected", {
       Species = "Species"
     )
   )
+  expect_equal(
+    var_label(df, null_action = "na"),
+    list(
+      Sepal.Length = NA_character_,
+      Sepal.Width = NA_character_,
+      Petal.Length = "length of petal",
+      Petal.Width = "width of petal",
+      Species = NA_character_
+    )
+  )
+  expect_equal(
+    var_label(df, null_action = "empty"),
+    list(
+      Sepal.Length = "",
+      Sepal.Width = "",
+      Petal.Length = "length of petal",
+      Petal.Width = "width of petal",
+      Species = ""
+    )
+  )
   expect_equal(
     var_label(df, null_action = "skip"),
     list(
diff --git a/tests/testthat/test-update_with.r b/tests/testthat/test-update_with.r
index 53fc715..09bac17 100644
--- a/tests/testthat/test-update_with.r
+++ b/tests/testthat/test-update_with.r
@@ -20,6 +20,16 @@ test_that("update_variable_labels_with() works as expected", {
   expect_equal(var_label(tmp$Species), "SPECIES")
   expect_equal(var_label(tmp$Sepal.Length), "LENGTH OF SEPAL")
   expect_equal(var_label(tmp$Petal.Width), "Width of petal")
+
+  tmp <- df %>%
+    update_variable_labels_with(~ tolower(names(.x)))
+  expect_equal(var_label(tmp$Species), "species")
+  expect_equal(var_label(tmp$Sepal.Length), "sepal.length")
+
+  tmp <- iris %>%
+    update_variable_labels_with(~ tolower(names(.x)))
+  expect_equal(var_label(tmp$Species), "species")
+  expect_equal(var_label(tmp$Sepal.Length), "sepal.length")
 })
 
 test_that("update_value_labels_with() works as expected", {