diff --git a/swh/storage/tests/test_api_client.py b/swh/storage/tests/test_api_client.py
--- a/swh/storage/tests/test_api_client.py
+++ b/swh/storage/tests/test_api_client.py
@@ -20,7 +20,7 @@
 from swh.storage.db import Db
 from swh.storage.tests.test_storage import (
     TestStorage as _TestStorage,
-    TestStorageCommonProp as _TestStorageCommonProp,
+    TestStorageGeneratedData as _TestStorageCommonProp,
     StorageTestDbFixture)
 
 
diff --git a/swh/storage/tests/test_in_memory.py b/swh/storage/tests/test_in_memory.py
--- a/swh/storage/tests/test_in_memory.py
+++ b/swh/storage/tests/test_in_memory.py
@@ -10,7 +10,7 @@
 
 from swh.storage.tests.test_storage import (
     TestStorage as _TestStorage,
-    TestStorageCommonProp as _TestStorageCommonProp)
+    TestStorageGeneratedData as _TestStorageCommonProp)
 
 
 @pytest.mark.xfail
diff --git a/swh/storage/tests/test_storage.py b/swh/storage/tests/test_storage.py
--- a/swh/storage/tests/test_storage.py
+++ b/swh/storage/tests/test_storage.py
@@ -90,7 +90,7 @@
 
 
 class TestStorage:
-    """Base class for Storage testing.
+    """Main class for Storage testing.
 
     This class is used as-is to test local storage (see TestLocalStorage
     below) and remote storage (see TestRemoteStorage in
@@ -3010,7 +3010,7 @@
         assert m_by_provider == expected_results
 
 
-class TestStorageCommonProp:
+class TestStorageGeneratedData:
     _test_origin_ids = True
 
     def assert_contents_ok(self, expected_contents, actual_contents,