When ARR came out they give everyone free race/name change then some people did not get it so they give them a fantasia item for the race change. Then they offer a way to change there name for a limit time only and i'm pretty sure they no longer doing it. You would have to wait for them to sell name change so far they going to add fantasia but that only for race and i'm pretty sure name is not in that.

There other way t odo it but would mean you have to switch worlds then switch back which would cost you money and time. So i think i would stay with your name one day they offer a way to change it.