feat: Implement Nakama serialization, Realtime API, and a comprehensive lobby system with UI and player management.

scripts/managers/lobby_manager.gd

@@ -277,6 +277,37 @@ func sync_character(player_id: int, character_name: String) -> void:
 	emit_signal("character_changed", player_id, character_name)
 	emit_signal("player_list_changed")
 
+# =============================================================================
+# Player Name Management
+# =============================================================================
+
+func set_player_name(new_name: String) -> void:
+	"""Set local player's name. Syncs to all peers."""
+	local_player_name = new_name
+	var my_id = multiplayer.get_unique_id()
+	
+	# Update local player data
+	for player in players_in_room:
+		if player["id"] == my_id:
+			player["name"] = new_name
+			break
+	
+	# Sync to all peers if connected
+	if multiplayer.has_multiplayer_peer():
+		rpc("sync_player_name", my_id, new_name)
+	
+	emit_signal("player_list_changed")
+
+@rpc("any_peer", "call_local", "reliable")
+func sync_player_name(player_id: int, new_name: String) -> void:
+	"""Sync player name across all clients."""
+	for player in players_in_room:
+		if player["id"] == player_id:
+			player["name"] = new_name
+			break
+	
+	emit_signal("player_list_changed")
+
 # =============================================================================
 # Area Selection (Host Only)
 # =============================================================================