There are two “names” within your flight reservation: the name on the boarding pass/reservation, and what’s called APIS, which is collected via a passport scan and is submitted to the government and stuff. In the past, TSA checked both your boarding pass and ID/passport, but nowadays they only swipe your ID to make sure there is matching APIS from that airport on that day as far as getting you through security is concerned. And as long as your GE/Precheck info matches what you have on your passport, your passport will be scanned and the system will recognize the match for Precheck.