how to transfer variables from lobby player to game player on client

i use this code on LobbyManager to transfer variables from lobby player to game player:

 public override bool OnLobbyServerSceneLoadedForPlayer(GameObject lobbyPlayer, GameObject gamePlayer) 
 {        
      gamePlayer.name = lobbyPlayer.name;
 }

but, it worked only on server. and it dos not let me to call command on gamePlayer because its not local player!

is there any other function like OnLobbyServerSceneLoadedForPlayer, that call on all client? or any other way to transfer variables from lobby player to game player?