USCIS does not have the authority to change a person’s name when they naturalize.   However, you can request that USCIS issues a Certificate of Naturalization under a new name if:

• You present proof that you have already legally changed your name.   Such proof could be a Marriage Certificate, Divorce Decree or Court Order with your new name.
• You take the Oath of Allegiance at a Naturalization Ceremony that is held in a Court.   Then, you can ask the Court to change your name.   If the Court grants your request, your new name will be in the Certificate