Hello, and welcome!
While your name on all ID's and airline tickets/boarding passes should be the same, and the same as your enrollment information, using your driver's license, which only has a middle initial and not your full middle name, should not cause a problem going through TSA screening. However, since you enrolled in a TSA program with your passport, showing your full middle name, it would be a good idea to use that as your primary government issued, photo ID, when going through TSA security screening, to avoid any problems or delays. You can actually show your driver's license and if there is any doubt regarding your middle initial vs. full middle name, then, you can show your passport.
I hope this helped and wish you safe travel!
Please be so kind as to rate my answer positively, as that is the only way I receive credit for my assistance. Thank you very much!Rating will not cut off our communication and you can click 'Reply' at any time, to ask for clarification or additional information.Warmest regards,Cher