Hello, and thanks for requesting me to help with your question.
Do you have a GOES card and included with that, is TSA Precheck, with a KTN?
If you're going to get a new passport with a name change and you have also changed your name on your driver's license and social security card, if you currently have a GOES card, you don't have to go through the entire registration process again, but you can update your information in your GOES profile to reflect your new passport information; you will have to provide them with all the documents leading to your name change (marriage, divorce, etc.) and pay a $25 fee to receive a new GOES card reflecting your new information, PASSID OR KTN.
If you don't have a GOES card or TSA Precheck yet, and are applying for Precheck for the first time, resulting in the issuance of a KTN, don't apply until you renew your passport with your name change and then all documents will have the same information and you shouldn't encounter any problems. Just keep in mind that everything needs to match.
I hope this helped and if so, please rate positively so I receive credit for my assistance. Thank you very much.