If a lesbian or gay couple wants to have the same surname they may do so. In North Carolina, anyone may use a different name as long as he or she is not doing so in order to defraud creditors. A couple may hyphenate their two names or choose an entirely different name to use.
However, no person, agency or business is required to accept your chosen name. The Division of Motor Vehicles, for example, probably will insist that your driver's license be in your "legal" name, which is the name on your birth or marriage certificate. Most creditors also will want to extend credit in your legal name. For social purposes you can be whoever you choose to be.
It is possible to file a petition to change your name to a new legal name. You are required to state a reason for the name change although it is rare for a clerk to deny a name change for an insufficient reason. Moreover, in North Carolina such a change may only be made once. So ordinarily it is not an advisable procedure.