Are you referring to your in-game username? If so you have to purchase a name change. https://www.planetside2.com/character-services If you're referring to your forum username, I don't think there is a way to do it though I'm probably blind.
Since Daybreak-Cash is an ingame-currency that you can use like an Pre-Paid Card that means you bought DBG-Cash already. Also DBG-Cash is not refundable, so you need to use money from your Bank.
Yeah yeah..I figured that out on my own. A name is used in-game so I don't see why it would not be setup to allow me to pay for a new name using battle cash. Just poorly designed IMO. But, thanx for the reply.