diff --git a/swh/storage/__init__.py b/swh/storage/__init__.py
--- a/swh/storage/__init__.py
+++ b/swh/storage/__init__.py
@@ -54,7 +54,7 @@
     elif cls == 'local':
         from .storage import Storage
     elif cls == 'memory':
-        from .in_memory import Storage
+        from .in_memory import InMemoryStorage as Storage
     elif cls == 'filter':
         from .filter import FilteringProxyStorage as Storage
     elif cls == 'buffer':
diff --git a/swh/storage/in_memory.py b/swh/storage/in_memory.py
--- a/swh/storage/in_memory.py
+++ b/swh/storage/in_memory.py
@@ -37,7 +37,7 @@
     return datetime.datetime.now(tz=datetime.timezone.utc)
 
 
-class Storage:
+class InMemoryStorage:
     def __init__(self, journal_writer=None):
         self._contents = {}
         self._content_indexes = defaultdict(lambda: defaultdict(set))
diff --git a/swh/storage/tests/algos/test_origin.py b/swh/storage/tests/algos/test_origin.py
--- a/swh/storage/tests/algos/test_origin.py
+++ b/swh/storage/tests/algos/test_origin.py
@@ -5,7 +5,7 @@
 
 from unittest.mock import patch
 
-from swh.storage.in_memory import Storage
+from swh.storage.in_memory import InMemoryStorage
 from swh.storage.algos.origin import iter_origins
 
 
@@ -14,7 +14,7 @@
 
 
 def test_iter_origins():
-    storage = Storage()
+    storage = InMemoryStorage()
     origins = storage.origin_add([
         {'url': 'bar'},
         {'url': 'qux'},
@@ -60,9 +60,9 @@
                 (i, j))
 
 
-@patch('swh.storage.in_memory.Storage.origin_get_range')
+@patch('swh.storage.in_memory.InMemoryStorage.origin_get_range')
 def test_iter_origins_batch_size(mock_origin_get_range):
-    storage = Storage()
+    storage = InMemoryStorage()
     mock_origin_get_range.return_value = []
 
     list(iter_origins(storage))
diff --git a/swh/storage/tests/test_init.py b/swh/storage/tests/test_init.py
--- a/swh/storage/tests/test_init.py
+++ b/swh/storage/tests/test_init.py
@@ -11,7 +11,7 @@
 
 from swh.storage.api.client import RemoteStorage
 from swh.storage.storage import Storage as DbStorage
-from swh.storage.in_memory import Storage as MemoryStorage
+from swh.storage.in_memory import InMemoryStorage
 from swh.storage.buffer import BufferingProxyStorage
 from swh.storage.filter import FilteringProxyStorage
 from swh.storage.retry import RetryingProxyStorage
@@ -25,7 +25,7 @@
     mock_pool.ThreadedConnectionPool.return_value = None
     for cls, real_class, dummy_args in [
             ('remote', RemoteStorage, {'url': 'url'}),
-            ('memory', MemoryStorage, {}),
+            ('memory', InMemoryStorage, {}),
             ('local', DbStorage, {
                 'db': 'postgresql://db', 'objstorage': {
                     'cls': 'memory', 'args': {},
@@ -55,7 +55,7 @@
     mock_pool.ThreadedConnectionPool.return_value = None
     for cls, real_class, dummy_args in [
             ('remote', RemoteStorage, {'url': 'url'}),
-            ('memory', MemoryStorage, {}),
+            ('memory', InMemoryStorage, {}),
             ('local', DbStorage, {
                 'db': 'postgresql://db', 'objstorage': {
                     'cls': 'memory', 'args': {},
@@ -105,7 +105,7 @@
 
     assert isinstance(storage, FilteringProxyStorage)
     assert isinstance(storage.storage, BufferingProxyStorage)
-    assert isinstance(storage.storage.storage, MemoryStorage)
+    assert isinstance(storage.storage.storage, InMemoryStorage)
 
 
 def test_get_storage_pipeline_legacy_args():
@@ -134,4 +134,4 @@
 
     assert isinstance(storage, FilteringProxyStorage)
     assert isinstance(storage.storage, BufferingProxyStorage)
-    assert isinstance(storage.storage.storage, MemoryStorage)
+    assert isinstance(storage.storage.storage, InMemoryStorage)
diff --git a/swh/storage/tests/test_retry.py b/swh/storage/tests/test_retry.py
--- a/swh/storage/tests/test_retry.py
+++ b/swh/storage/tests/test_retry.py
@@ -44,7 +44,8 @@
     """Multiple retries for hash collision and psycopg2 error but finally ok
 
     """
-    mock_memory = mocker.patch('swh.storage.in_memory.Storage.content_add')
+    mock_memory = mocker.patch(
+        'swh.storage.in_memory.InMemoryStorage.content_add')
     mock_memory.side_effect = [
         # first try goes ko
         HashCollision('content hash collision'),
@@ -74,7 +75,8 @@
     """Unfiltered errors are raising without retry
 
     """
-    mock_memory = mocker.patch('swh.storage.in_memory.Storage.content_add')
+    mock_memory = mocker.patch(
+        'swh.storage.in_memory.InMemoryStorage.content_add')
     mock_memory.side_effect = ValueError('Refuse to add content always!')
 
     sample_content = sample_data['content'][0]
@@ -115,7 +117,7 @@
 
     """
     mock_memory = mocker.patch(
-        'swh.storage.in_memory.Storage.content_add_metadata')
+        'swh.storage.in_memory.InMemoryStorage.content_add_metadata')
     mock_memory.side_effect = [
         # first try goes ko
         HashCollision('content_metadata hash collision'),
@@ -143,7 +145,7 @@
 
     """
     mock_memory = mocker.patch(
-        'swh.storage.in_memory.Storage.content_add_metadata')
+        'swh.storage.in_memory.InMemoryStorage.content_add_metadata')
     mock_memory.side_effect = ValueError('Refuse to add content_metadata!')
 
     sample_content = sample_data['content_metadata'][0]
@@ -180,7 +182,8 @@
 
     """
     sample_origin = sample_data['origin'][1]
-    mock_memory = mocker.patch('swh.storage.in_memory.Storage.origin_add_one')
+    mock_memory = mocker.patch(
+        'swh.storage.in_memory.InMemoryStorage.origin_add_one')
     mock_memory.side_effect = [
         # first try goes ko
         HashCollision('origin hash collision'),
@@ -208,7 +211,8 @@
     """Unfiltered errors are raising without retry
 
     """
-    mock_memory = mocker.patch('swh.storage.in_memory.Storage.origin_add_one')
+    mock_memory = mocker.patch(
+        'swh.storage.in_memory.InMemoryStorage.origin_add_one')
     mock_memory.side_effect = ValueError('Refuse to add origin always!')
 
     sample_origin = sample_data['origin'][0]
@@ -253,7 +257,7 @@
     origin_url = sample_origin['url']
 
     mock_memory = mocker.patch(
-        'swh.storage.in_memory.Storage.origin_visit_add')
+        'swh.storage.in_memory.InMemoryStorage.origin_visit_add')
     mock_memory.side_effect = [
         # first try goes ko
         HashCollision('origin hash collision'),
@@ -282,7 +286,7 @@
 
     """
     mock_memory = mocker.patch(
-        'swh.storage.in_memory.Storage.origin_visit_add')
+        'swh.storage.in_memory.InMemoryStorage.origin_visit_add')
     mock_memory.side_effect = ValueError('Refuse to add origin always!')
 
     origin_url = sample_data['origin'][0]['url']
@@ -324,7 +328,8 @@
 
     """
     sample_tool = sample_data['tool'][0]
-    mock_memory = mocker.patch('swh.storage.in_memory.Storage.tool_add')
+    mock_memory = mocker.patch(
+        'swh.storage.in_memory.InMemoryStorage.tool_add')
     mock_memory.side_effect = [
         # first try goes ko
         HashCollision('tool hash collision'),
@@ -352,7 +357,8 @@
     """Unfiltered errors are raising without retry
 
     """
-    mock_memory = mocker.patch('swh.storage.in_memory.Storage.tool_add')
+    mock_memory = mocker.patch(
+        'swh.storage.in_memory.InMemoryStorage.tool_add')
     mock_memory.side_effect = ValueError('Refuse to add tool always!')
 
     sample_tool = sample_data['tool'][0]
@@ -405,7 +411,7 @@
     provider_get = to_provider(provider)
 
     mock_memory = mocker.patch(
-        'swh.storage.in_memory.Storage.metadata_provider_add')
+        'swh.storage.in_memory.InMemoryStorage.metadata_provider_add')
     mock_memory.side_effect = [
         # first try goes ko
         HashCollision('provider_id hash collision'),
@@ -434,7 +440,7 @@
 
     """
     mock_memory = mocker.patch(
-        'swh.storage.in_memory.Storage.metadata_provider_add')
+        'swh.storage.in_memory.InMemoryStorage.metadata_provider_add')
     mock_memory.side_effect = ValueError('Refuse to add provider_id always!')
 
     provider = sample_data['provider'][0]
@@ -483,7 +489,7 @@
     provider_get = to_provider(ori_meta['provider'])
     provider_id = swh_storage.metadata_provider_add(**provider_get)
     mock_memory = mocker.patch(
-        'swh.storage.in_memory.Storage.origin_metadata_add')
+        'swh.storage.in_memory.InMemoryStorage.origin_metadata_add')
 
     mock_memory.side_effect = [
         # first try goes ko
@@ -515,7 +521,7 @@
 
     """
     mock_memory = mocker.patch(
-        'swh.storage.in_memory.Storage.origin_metadata_add')
+        'swh.storage.in_memory.InMemoryStorage.origin_metadata_add')
     mock_memory.side_effect = ValueError('Refuse to add always!')
 
     ori_meta = sample_data['origin_metadata'][0]
@@ -572,7 +578,7 @@
     origin_url = sample_origin['url']
 
     mock_memory = mocker.patch(
-        'swh.storage.in_memory.Storage.origin_visit_update')
+        'swh.storage.in_memory.InMemoryStorage.origin_visit_update')
     mock_memory.side_effect = [
         # first try goes ko
         HashCollision('origin hash collision'),
@@ -598,7 +604,7 @@
 
     """
     mock_memory = mocker.patch(
-        'swh.storage.in_memory.Storage.origin_visit_update')
+        'swh.storage.in_memory.InMemoryStorage.origin_visit_update')
     mock_memory.side_effect = ValueError('Refuse to add origin always!')
     origin_url = sample_data['origin'][0]['url']
     visit_id = 9
@@ -632,7 +638,8 @@
     """Multiple retries for hash collision and psycopg2 error but finally ok
 
     """
-    mock_memory = mocker.patch('swh.storage.in_memory.Storage.directory_add')
+    mock_memory = mocker.patch(
+        'swh.storage.in_memory.InMemoryStorage.directory_add')
     mock_memory.side_effect = [
         # first try goes ko
         HashCollision('directory hash collision'),
@@ -664,7 +671,8 @@
     """Unfiltered errors are raising without retry
 
     """
-    mock_memory = mocker.patch('swh.storage.in_memory.Storage.directory_add')
+    mock_memory = mocker.patch(
+        'swh.storage.in_memory.InMemoryStorage.directory_add')
     mock_memory.side_effect = ValueError('Refuse to add directory always!')
 
     sample_dir = sample_data['directory'][0]
@@ -701,7 +709,8 @@
     """Multiple retries for hash collision and psycopg2 error but finally ok
 
     """
-    mock_memory = mocker.patch('swh.storage.in_memory.Storage.revision_add')
+    mock_memory = mocker.patch(
+        'swh.storage.in_memory.InMemoryStorage.revision_add')
     mock_memory.side_effect = [
         # first try goes ko
         HashCollision('revision hash collision'),
@@ -733,7 +742,8 @@
     """Unfiltered errors are raising without retry
 
     """
-    mock_memory = mocker.patch('swh.storage.in_memory.Storage.revision_add')
+    mock_memory = mocker.patch(
+        'swh.storage.in_memory.InMemoryStorage.revision_add')
     mock_memory.side_effect = ValueError('Refuse to add revision always!')
 
     sample_rev = sample_data['revision'][0]
@@ -770,7 +780,8 @@
     """Multiple retries for hash collision and psycopg2 error but finally ok
 
     """
-    mock_memory = mocker.patch('swh.storage.in_memory.Storage.release_add')
+    mock_memory = mocker.patch(
+        'swh.storage.in_memory.InMemoryStorage.release_add')
     mock_memory.side_effect = [
         # first try goes ko
         HashCollision('release hash collision'),
@@ -802,7 +813,8 @@
     """Unfiltered errors are raising without retry
 
     """
-    mock_memory = mocker.patch('swh.storage.in_memory.Storage.release_add')
+    mock_memory = mocker.patch(
+        'swh.storage.in_memory.InMemoryStorage.release_add')
     mock_memory.side_effect = ValueError('Refuse to add release always!')
 
     sample_rel = sample_data['release'][0]
@@ -839,7 +851,8 @@
     """Multiple retries for hash collision and psycopg2 error but finally ok
 
     """
-    mock_memory = mocker.patch('swh.storage.in_memory.Storage.snapshot_add')
+    mock_memory = mocker.patch(
+        'swh.storage.in_memory.InMemoryStorage.snapshot_add')
     mock_memory.side_effect = [
         # first try goes ko
         HashCollision('snapshot hash collision'),
@@ -871,7 +884,8 @@
     """Unfiltered errors are raising without retry
 
     """
-    mock_memory = mocker.patch('swh.storage.in_memory.Storage.snapshot_add')
+    mock_memory = mocker.patch(
+        'swh.storage.in_memory.InMemoryStorage.snapshot_add')
     mock_memory.side_effect = ValueError('Refuse to add snapshot always!')
 
     sample_snap = sample_data['snapshot'][0]