If you wanted to change your name, you could have done that at the citizenship ceremony. You are welcome to do so now at the state court if you feel you must.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.
You will need to go through the State procedure to correct your name...
Att. number 917-885-2261 This advice does not create an attorney client relationship. No specific legal advice may be offered by the lawyer until a conflicts check is undertaken. Information sent through a web form or via email may not be treated as confidential. Please accept my apologies for spelling mistakes. Law Office of Alena Shautsova , New York Immigration Attorney http://www.shautsova.com Blog: http://www.russianspeakinglawyerny.com
This depends on how you completed the N-400. If you listed your name on page one under "Family Name" as your married then maiden, then you made an error on your application (or if you mistakenly listed your maiden name under Family Name and your married name under Middle?). If you listed it correctly on your N-400, then at some point an error may have been made by USCIS. During your Naturalization interview, the officer should have had you look at a piece of paper with your information on it and asked you to verify - that information is what goes on your certificate and if you verified incorrect information, then it is not USCIS' error. If you requested a legal name change (that would not be necessary if you are changing to your married name), that could also be where the error occurred if you listed your new name incorrectly.
This is not something that is very easily determined if you are not familiar with how to go about finding out (and especially if you did not keep a copy of your entire application) and if you want to address this most efficiently, you should get an immigration attorney's help. If it is determined that USCIS made no error, you would be responsible for paying for the correction. If it is determined that it is USCIS error, then you would be able to get a replacement based on the error at no fee.