Disambiguate displaynames (#2918)

* Disambigute displaynames

* Add test

* fixup test functions

* prettier

* lint

* Split displayname utils into own file and add tests.

* Split out fixtures

* Add more testcases for displayname calculation.

* lint

* Also listen for displayname changes. (I stand corrected!)

* fix missing media tiles on missing member

src/utils/test.ts

@@ -205,6 +205,7 @@ export async function withLocalMedia(
       kind: E2eeType.PER_PARTICIPANT,
     },
     mockLivekitRoom({ localParticipant }),
+    of(roomMember.rawDisplayName ?? "nodisplayname"),
     of(null),
     of(null),
   );
@@ -243,6 +244,7 @@ export async function withRemoteMedia(
       kind: E2eeType.PER_PARTICIPANT,
     },
     mockLivekitRoom({}, { remoteParticipants$: of([remoteParticipant]) }),
+    of(roomMember.rawDisplayName ?? "nodisplayname"),
     of(null),
     of(null),
   );