Upvote:7
If you're paying for your passport application in the United States, you make your check or money order payable to "U.S. Department of State". The USPS advised me when I went in this year that your name and date of birth should appear on the check/money order (in case it gets separated from your application).
You must also pay a separate $35 execution fee to the agency which accepts your passport application (this fee was $25 prior to April 2018). This must be made payable to the agency accepting your application, but most such agencies will accept debit/credit cards for this payment.
If you're paying for your passport outside the United States, contact the embassy or consulate for payment instructions.