I thought this might help those of us considering a legal name change.
The N400 application is (in most cases) a great time to legally change your name. It's fast and it's free. Outside of the N400 process, a name change requires a visit to your local courthouse, may require a public announcement in a newspaper (depending on your state and local laws) and will cost you money. In New York City, the cost is about $65 while on Houston it is over $400, so cost varies from city to city.
You can change your name to anything you want within certain limitations. You can't change your name to impersonate someone or in an attempt to hide your identity for illegal purposes. Other than that, it's up to you. If you are Arthur Robert Wilkinson, you can become Geraldo Mohamed Leibowitz.
It's important to note that if you are just changing your last name to take your spouse's last name or to revert to your maiden name, then a legal name change is not required. This is because a marriage certificate or a divorce certificate acts as proof of legal name change. This is true EVEN IF your certificate does not show the new name that you want to take. For example, if Anita Mary Harrolds marries Geraldo Mohamed Leibowitz, she can legally be known as Anita Mary Leibowitz even though that name does not appear anywhere on the certificate. In fact, she can also hyphenate both last names without a legal name change. However, if she wanted to change her middle name from Mary to Margaret, she would need a legal name change.
To request a legal name change through the naturalization process, fill out the name change section of the N400. The interviewer may ask you to confirm that you still want to change your name because some people change their minds between the application and the interview. The interviewer may ask for proof of your current legal name. In case of a discrepancy between your green card and your passport, a birth, marriage, divorce, or name change certificate determines your current name, so make sure you have these with you (if they apply in your case...it's always a good idea to have your translated birth certificate with you at the interview). The interviewer will print out some forms (three I think) for you to check and sign. These should have your old and new names on them.
You will have to be scheduled for a judicial oath ceremony. This is because USCIS does not have the legal authority to change your name and must ask a judge to do so. If your city has regular judicial ceremonies then there shouldn't be any delays. If your city holds regular administrative ceremonies, but not many judicial ceremonies, then the name change may cause a delay. Some cities (including San Francisco and San Jose) have stopped scheduling judicial ceremonies altogether. Applicants in these cities cannot legally change their names through the N400 application. Your interviewer will inform you of this and will cross out the name change section during the interview. You will have to request a regular name change before or after naturalization if you live in these cities (see above).
At your oath ceremony you will be given your naturalization certificate as well as a name change certificate signed by a judge. This second certificate will show your old and new names and you'll need it to update your name with your banks, on your drivers license, credit cards, etc. In addition to doing all the paperwork to make these changes, you'll also have to consider the effect of the name change if you have dual citizenship; your name on your two passports may not match and your other country may require you to go through different name change procedures or may not allow name changes at all. People do travel using passports with different names, but you have to be careful when booking tickets and you may want to travel with your name change certificate (and translations).
If you want to check whether or not (and how often) judicial ceremonies are held in your location, find your office here and look under naturalization ceremonies: