Sync player name (Networking)

I'm using the new networking system and I can't really figure out how to display each player's name for all clients. The problem is that each client does not see the other clients name. I'm using these methods:

 public string playerName;

 public override void OnStartLocalPlayer() 
 {
     playerName = PlayerPrefs.GetString("PlayerName");

     // Give the server my name
     CmdProvideName(playerName);
 }

 [Command]
 void CmdProvideName(string name)
 {
     playerName = name;

     // Broadcast to all clients
     RpcPlayerName(name);
 }

 [ClientRpc]
 void RpcPlayerName(string name)
 {
     playerNameUI.GetComponent<Text>().text = name;
 }

 void Update()
 {
     // Keep the name updated for incoming connections
     RpcPlayerName(playerName);
 }

What's a good way to approach this? Thanks in advance!