diff --git a/swh/lister/gitlab/lister.py b/swh/lister/gitlab/lister.py
--- a/swh/lister/gitlab/lister.py
+++ b/swh/lister/gitlab/lister.py
@@ -97,16 +97,17 @@
 
     """
 
-    LISTER_NAME = "gitlab"
-
     def __init__(
         self,
         scheduler,
         url: str,
+        name: Optional[str] = "gitlab",
         instance: Optional[str] = None,
         credentials: Optional[CredentialsType] = None,
         incremental: bool = False,
     ):
+        if name is not None:
+            self.LISTER_NAME = name
         super().__init__(
             scheduler=scheduler,
             url=url.rstrip("/"),
diff --git a/swh/lister/gitlab/tests/test_lister.py b/swh/lister/gitlab/tests/test_lister.py
--- a/swh/lister/gitlab/tests/test_lister.py
+++ b/swh/lister/gitlab/tests/test_lister.py
@@ -57,11 +57,16 @@
 
 
 def test_lister_gitlab_heptapod(datadir, swh_scheduler, requests_mock):
-    """Gitlab lister ignores some vcs_type
+    """Heptapod lister happily lists hg, hg_git as hg and git origins
 
     """
+    name = "heptapod"
     instance = "foss.heptapod.net"
-    lister = GitLabLister(swh_scheduler, url=api_url(instance), instance=instance)
+    lister = GitLabLister(
+        swh_scheduler, url=api_url(instance), name=name, instance=instance
+    )
+    assert lister.LISTER_NAME == name
+
     response = gitlab_page_response(datadir, instance, 1)
 
     requests_mock.get(