diff --git a/src/ansys/meshing/prime/internals/launcher.py b/src/ansys/meshing/prime/internals/launcher.py
index 5656b9a3fc..15c54a8430 100644
--- a/src/ansys/meshing/prime/internals/launcher.py
+++ b/src/ansys/meshing/prime/internals/launcher.py
@@ -226,8 +226,9 @@ def launch_prime(
     if ip == defaults.ip():
         port = utils.get_available_local_port(port)
 
-    if 'PYPRIMEMESH_LAUNCH_CONTAINER' in os.environ:
-        container_name = 'ansys-prime-server'
+    launch_container = bool(int(os.environ.get('PYPRIMEMESH_LAUNCH_CONTAINER', '0')))
+    if launch_container:
+        container_name = utils.make_unique_container_name('ansys-prime-server')
         utils.launch_prime_github_container(port=port, name=container_name, version=version)
         config.set_using_container(True)
         client = Client(port=port, timeout=timeout)
diff --git a/src/ansys/meshing/prime/internals/utils.py b/src/ansys/meshing/prime/internals/utils.py
index eac62a7b2e..b1ad6f9e1b 100644
--- a/src/ansys/meshing/prime/internals/utils.py
+++ b/src/ansys/meshing/prime/internals/utils.py
@@ -10,6 +10,25 @@
 import ansys.meshing.prime.internals.defaults as defaults
 
 _LOCAL_PORTS = []
+_PRIME_CONTAINER_COUNT = 0
+
+
+def make_unique_container_name(name: str):
+    """Make a unique container name.
+
+    Parameters
+    ----------
+    name : str
+        Original name prefix that is provided.
+
+    Returns
+    -------
+    str
+        Unique name with a numeric integer added as suffix.
+    """
+    global _PRIME_CONTAINER_COUNT
+    _PRIME_CONTAINER_COUNT = _PRIME_CONTAINER_COUNT + 1
+    return f'{name}-{_PRIME_CONTAINER_COUNT}'
 
 
 def to_camel_case(snake_str):