Not only must you notify them of your name change, you must also bring the proper proof of identification including all the proper documentation which goes along with it.
It is important the department of motor vehicles has your proper name and address in the event they need to make contact with you for something. Plus, in many cases the postal service will not forward mail from the department of motor vehicle so if you do not let them know what your correct address is, you simply will not get the license and registration renewal information from them; or the notice that your driving privileges have been suspended.
You are required by law to notify MVD of a name or address change within 10 days. We are required to verify your Social Security Number before your record can be updated, therefore you must first contact the Social Security Administration online or at 800-772-1213 for information on how to change your name on their records. After you have changed your name with SSA, wait two days for their computer system to be updated. You should then visit an MVD office to present identification in both your new and previous names. This must be an original or certified copy (must be certified by the issuing agency) of one of the following: Marriage Certificate/License, Divorce Decree, Certificate of Citizenship/Naturalization or a court order.