If your most recent U.S. passport was issued less than one year ago, use form DS-5504 (Name Change Form). Include certified evidence of name change or other change in descriptive data and one new passport photo and mail it to address on form to get a new passport free of charge.
If your valid U.S. passport was issued more than one year ago, use form DS-82 (Renewal Form). Include certified evidence of name change or other change in descriptive data, one new photo and a check, and mail it to address on form.