feat: Implement core multiplayer lobby system with room management, player profiles, and game settings.

scripts/managers/lobby_manager.gd

@@ -293,7 +293,7 @@ func set_player_name(new_name: String) -> void:
 			break
 	
 	# Sync to all peers if connected
-	if multiplayer.has_multiplayer_peer():
+	if multiplayer.has_multiplayer_peer() and multiplayer.multiplayer_peer.get_connection_status() == MultiplayerPeer.CONNECTION_CONNECTED:
 		rpc("sync_player_name", my_id, new_name)
 	
 	emit_signal("player_list_changed")

scripts/managers/user_profile_manager.gd

@@ -120,17 +120,25 @@ func load_stats() -> Dictionary:
 # =============================================================================
 
 func update_display_name(new_name: String) -> bool:
-	if not NakamaManager.session:
-		emit_signal("profile_update_failed", "Not authenticated")
-		return false
-	
 	if new_name.strip_edges().is_empty():
 		emit_signal("profile_update_failed", "Display name cannot be empty")
 		return false
 	
-	if new_name.length() > 50:
-		emit_signal("profile_update_failed", "Display name too long (max 50 characters)")
+	if new_name.length() > 6:
+		emit_signal("profile_update_failed", "Display name too long (max 6 characters)")
 		return false
+		
+	var regex = RegEx.new()
+	regex.compile("^[A-Za-z]+$")
+	if not regex.search(new_name):
+		emit_signal("profile_update_failed", "Name must contain only letters")
+		return false
+
+	# Allow guest name updates locally
+	if not NakamaManager.session or AuthManager.is_guest:
+		profile["display_name"] = new_name
+		emit_signal("profile_updated")
+		return true
 	
 	var result: NakamaAsyncResult = await NakamaManager.client.update_account_async(
 		NakamaManager.session,