diff --git a/changelog.d/12036.misc b/changelog.d/12036.misc
new file mode 100644
index 0000000000000000000000000000000000000000..d2996730cc2c3c4aaa98cd3748c98c2cf3cec969
--- /dev/null
+++ b/changelog.d/12036.misc
@@ -0,0 +1 @@
+Rename `shared_rooms` to `mutual_rooms` (MSC2666), as per proposal changes.
\ No newline at end of file
diff --git a/synapse/rest/__init__.py b/synapse/rest/__init__.py
index 762808a5717b6c06101ce202a03ee760bc3d7513..57c4773edce6ff0e56e710a76f5f5771f89282d2 100644
--- a/synapse/rest/__init__.py
+++ b/synapse/rest/__init__.py
@@ -32,6 +32,7 @@ from synapse.rest.client import (
     knock,
     login as v1_login,
     logout,
+    mutual_rooms,
     notifications,
     openid,
     password_policy,
@@ -49,7 +50,6 @@ from synapse.rest.client import (
     room_keys,
     room_upgrade_rest_servlet,
     sendtodevice,
-    shared_rooms,
     sync,
     tags,
     thirdparty,
@@ -132,4 +132,4 @@ class ClientRestResource(JsonResource):
         admin.register_servlets_for_client_rest_resource(hs, client_resource)
 
         # unstable
-        shared_rooms.register_servlets(hs, client_resource)
+        mutual_rooms.register_servlets(hs, client_resource)
diff --git a/synapse/rest/client/shared_rooms.py b/synapse/rest/client/mutual_rooms.py
similarity index 88%
rename from synapse/rest/client/shared_rooms.py
rename to synapse/rest/client/mutual_rooms.py
index e669fa78902d557c66be32d5e676d6a33c730c6d..d3872a76c85c8079980a8e3d194e3f13b3ec1600 100644
--- a/synapse/rest/client/shared_rooms.py
+++ b/synapse/rest/client/mutual_rooms.py
@@ -28,13 +28,13 @@ if TYPE_CHECKING:
 logger = logging.getLogger(__name__)
 
 
-class UserSharedRoomsServlet(RestServlet):
+class UserMutualRoomsServlet(RestServlet):
     """
-    GET /uk.half-shot.msc2666/user/shared_rooms/{user_id} HTTP/1.1
+    GET /uk.half-shot.msc2666/user/mutual_rooms/{user_id} HTTP/1.1
     """
 
     PATTERNS = client_patterns(
-        "/uk.half-shot.msc2666/user/shared_rooms/(?P<user_id>[^/]*)",
+        "/uk.half-shot.msc2666/user/mutual_rooms/(?P<user_id>[^/]*)",
         releases=(),  # This is an unstable feature
     )
 
@@ -64,7 +64,8 @@ class UserSharedRoomsServlet(RestServlet):
                 msg="You cannot request a list of shared rooms with yourself",
                 errcode=Codes.FORBIDDEN,
             )
-        rooms = await self.store.get_shared_rooms_for_users(
+
+        rooms = await self.store.get_mutual_rooms_for_users(
             requester.user.to_string(), user_id
         )
 
@@ -72,4 +73,4 @@ class UserSharedRoomsServlet(RestServlet):
 
 
 def register_servlets(hs: "HomeServer", http_server: HttpServer) -> None:
-    UserSharedRoomsServlet(hs).register(http_server)
+    UserMutualRoomsServlet(hs).register(http_server)
diff --git a/synapse/storage/databases/main/user_directory.py b/synapse/storage/databases/main/user_directory.py
index 55cc9178f0b891b7c8ec5d493e92fade3ad76f84..0595df01d372fcfa3d2a025bfcd24f065d47d004 100644
--- a/synapse/storage/databases/main/user_directory.py
+++ b/synapse/storage/databases/main/user_directory.py
@@ -730,7 +730,7 @@ class UserDirectoryStore(UserDirectoryBackgroundUpdateStore):
         users.update(rows)
         return list(users)
 
-    async def get_shared_rooms_for_users(
+    async def get_mutual_rooms_for_users(
         self, user_id: str, other_user_id: str
     ) -> Set[str]:
         """
@@ -744,7 +744,7 @@ class UserDirectoryStore(UserDirectoryBackgroundUpdateStore):
             A set of room ID's that the users share.
         """
 
-        def _get_shared_rooms_for_users_txn(
+        def _get_mutual_rooms_for_users_txn(
             txn: LoggingTransaction,
         ) -> List[Dict[str, str]]:
             txn.execute(
@@ -768,7 +768,7 @@ class UserDirectoryStore(UserDirectoryBackgroundUpdateStore):
             return rows
 
         rows = await self.db_pool.runInteraction(
-            "get_shared_rooms_for_users", _get_shared_rooms_for_users_txn
+            "get_mutual_rooms_for_users", _get_mutual_rooms_for_users_txn
         )
 
         return {row["room_id"] for row in rows}
diff --git a/tests/rest/client/test_shared_rooms.py b/tests/rest/client/test_mutual_rooms.py
similarity index 87%
rename from tests/rest/client/test_shared_rooms.py
rename to tests/rest/client/test_mutual_rooms.py
index 3818b7b14bf34fd0789ef8ec2fb38aa189a35e16..7b7d283bb628a301f369ca8df85cc07b44208f76 100644
--- a/tests/rest/client/test_shared_rooms.py
+++ b/tests/rest/client/test_mutual_rooms.py
@@ -14,7 +14,7 @@
 from twisted.test.proto_helpers import MemoryReactor
 
 import synapse.rest.admin
-from synapse.rest.client import login, room, shared_rooms
+from synapse.rest.client import login, mutual_rooms, room
 from synapse.server import HomeServer
 from synapse.util import Clock
 
@@ -22,16 +22,16 @@ from tests import unittest
 from tests.server import FakeChannel
 
 
-class UserSharedRoomsTest(unittest.HomeserverTestCase):
+class UserMutualRoomsTest(unittest.HomeserverTestCase):
     """
-    Tests the UserSharedRoomsServlet.
+    Tests the UserMutualRoomsServlet.
     """
 
     servlets = [
         login.register_servlets,
         synapse.rest.admin.register_servlets_for_client_rest_resource,
         room.register_servlets,
-        shared_rooms.register_servlets,
+        mutual_rooms.register_servlets,
     ]
 
     def make_homeserver(self, reactor: MemoryReactor, clock: Clock) -> HomeServer:
@@ -43,10 +43,10 @@ class UserSharedRoomsTest(unittest.HomeserverTestCase):
         self.store = hs.get_datastores().main
         self.handler = hs.get_user_directory_handler()
 
-    def _get_shared_rooms(self, token: str, other_user: str) -> FakeChannel:
+    def _get_mutual_rooms(self, token: str, other_user: str) -> FakeChannel:
         return self.make_request(
             "GET",
-            "/_matrix/client/unstable/uk.half-shot.msc2666/user/shared_rooms/%s"
+            "/_matrix/client/unstable/uk.half-shot.msc2666/user/mutual_rooms/%s"
             % other_user,
             access_token=token,
         )
@@ -56,14 +56,14 @@ class UserSharedRoomsTest(unittest.HomeserverTestCase):
         A room should show up in the shared list of rooms between two users
         if it is public.
         """
-        self._check_shared_rooms_with(room_one_is_public=True, room_two_is_public=True)
+        self._check_mutual_rooms_with(room_one_is_public=True, room_two_is_public=True)
 
     def test_shared_room_list_private(self) -> None:
         """
         A room should show up in the shared list of rooms between two users
         if it is private.
         """
-        self._check_shared_rooms_with(
+        self._check_mutual_rooms_with(
             room_one_is_public=False, room_two_is_public=False
         )
 
@@ -72,9 +72,9 @@ class UserSharedRoomsTest(unittest.HomeserverTestCase):
         The shared room list between two users should contain both public and private
         rooms.
         """
-        self._check_shared_rooms_with(room_one_is_public=True, room_two_is_public=False)
+        self._check_mutual_rooms_with(room_one_is_public=True, room_two_is_public=False)
 
-    def _check_shared_rooms_with(
+    def _check_mutual_rooms_with(
         self, room_one_is_public: bool, room_two_is_public: bool
     ) -> None:
         """Checks that shared public or private rooms between two users appear in
@@ -94,7 +94,7 @@ class UserSharedRoomsTest(unittest.HomeserverTestCase):
 
         # Check shared rooms from user1's perspective.
         # We should see the one room in common
-        channel = self._get_shared_rooms(u1_token, u2)
+        channel = self._get_mutual_rooms(u1_token, u2)
         self.assertEqual(200, channel.code, channel.result)
         self.assertEqual(len(channel.json_body["joined"]), 1)
         self.assertEqual(channel.json_body["joined"][0], room_id_one)
@@ -107,7 +107,7 @@ class UserSharedRoomsTest(unittest.HomeserverTestCase):
         self.helper.join(room_id_two, user=u2, tok=u2_token)
 
         # Check shared rooms again. We should now see both rooms.
-        channel = self._get_shared_rooms(u1_token, u2)
+        channel = self._get_mutual_rooms(u1_token, u2)
         self.assertEqual(200, channel.code, channel.result)
         self.assertEqual(len(channel.json_body["joined"]), 2)
         for room_id_id in channel.json_body["joined"]:
@@ -128,7 +128,7 @@ class UserSharedRoomsTest(unittest.HomeserverTestCase):
         self.helper.join(room, user=u2, tok=u2_token)
 
         # Assert user directory is not empty
-        channel = self._get_shared_rooms(u1_token, u2)
+        channel = self._get_mutual_rooms(u1_token, u2)
         self.assertEqual(200, channel.code, channel.result)
         self.assertEqual(len(channel.json_body["joined"]), 1)
         self.assertEqual(channel.json_body["joined"][0], room)
@@ -136,11 +136,11 @@ class UserSharedRoomsTest(unittest.HomeserverTestCase):
         self.helper.leave(room, user=u1, tok=u1_token)
 
         # Check user1's view of shared rooms with user2
-        channel = self._get_shared_rooms(u1_token, u2)
+        channel = self._get_mutual_rooms(u1_token, u2)
         self.assertEqual(200, channel.code, channel.result)
         self.assertEqual(len(channel.json_body["joined"]), 0)
 
         # Check user2's view of shared rooms with user1
-        channel = self._get_shared_rooms(u2_token, u1)
+        channel = self._get_mutual_rooms(u2_token, u1)
         self.assertEqual(200, channel.code, channel.result)
         self.assertEqual(len(channel.json_body["joined"]), 0)