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)