Fill out Form DS-5504 if your passport was issued less than a year ago and if you've had a name change because of marriage or court order. Place the completed form, your current passport, an original or certified copy of your marriage license or government documentation proving your court-ordered name change and a recent photograph meeting passport specifications into a secure envelope. Mail the complete package to the address listed under the "How Do I Apply Using This Form" heading on page 2 of Form DS-5504.
Fill out Form DS-82 if your passport was issued over a year ago and you've had a name change by marriage or court order. Put the completed form, your current passport, your renewal fee, an original or certified copy of your marriage license or government documentation proving the legality of your name change and a recent photograph meeting passport specifications into a secure envelope. As of March 2011, the renewal fee is $110, and may be payed with a check or money order made out to the U.S. Department of State. Mail the complete package to the address found under the "Where Do I Send This Application" heading on Form DS-82.
Fill out Form DS-11 if you have no legal documentation of your name change or if you are under 16 with a passport issued over a year ago. You must have evidence of your U.S. citizenship, valid identification and clear photocopies of the front and back of the valid identification. Compile those documents, the completed form, application fees and a recent photograph meeting passport specifications. As of March 2011, first-time application fees for an adult passport include a $110 application fee and a $25 execution fee. For a minor they include an $80 application fee and a $25 application fee. Applications for this kind of name change must be submitted in-person at an Acceptance Facility or Passport Agency (see Resources for links to these sites).
Wait for your new passport to arrive. When it does, open it to page 2. There you should see your picture and your new name. Find your last name under "Surname/Nom/Apellidos." Find your first and middle name under "Given Name/Prenoms/Nombres."