I guess you're having the player set up as an actor and already joined to the active player group, otherwise you wont be able to change his name.
Now, in the Value Input Dialogue, you need to set Value Type to Value, because you're directly defining the name of the variable (e.g. type Game Variable will use the text stored in a game variable as the name of the variable you're using). Input type is, of course, String.
In the Set Combatant Name, enable Use Actor and select your player actor. This time, Value Type is Game Variable (because we want the text from the variable) and the Value is the name of your variable.
After that, the name of the combatant is set, but you can't display it using #combatant.name0#, because that'll only display the original name from the combatant's settings. #actor.name0# should display it.