I added both an identifier label above each head and a simple chat functionality to the Lobby. This was quite easy but changing scenes creashes the game. I guess that Godot (Engine) doesn’t like that as switching scripts redoes the whole thing.

@rpc("any_peer", "unreliable_ordered")
func _on_line_edit_text_submitted(new_text, origin = true):
	if len(new_text) < 1:
		return
	var who = multiplayer.get_unique_id()
	set_multiplayer_authority(who)
	if origin:
		new_text = str(who) + ": " + new_text + "\n"

	$Control/Panel/RichTextLabel.text += new_text
	$Control/LineEdit.text = ""
	
	if origin: # only the original sender tells the peers
		rpc("_on_line_edit_text_submitted", new_text, false)

The trick wswas to use a variazble to see if the sender was the the origin instead of a peer,