Most people seeking to change a passport should use the DS-82 form. Along with this form, submit certified documentation reflecting your name change. Note that you may need to use the DS-5504 form if one of these situations applies:
You changed your name less than one year since your passport was issued.
Identifying information was printed incorrectly on your most recent passport.
Your passport was limited to two years or less for a reason other than losing your passport multiple times or having a seriously damaged passport.
The cost varies depending on whether you are renewing the passport book or card. To complete this process, you can mail in your application with a check.