I am paying for the monthly AppleCare for my daughters iPhone XR and my oldest sons iPhone 14. AppleCare doesn’t care who foots the bill or what AppleID is logged in on the device. AppleCare is tied to the device Serial number.
Don’t bother asking at an Apple Store… you will be advised to contact 1-800-APL-CARE.
Just keep making the monthly payments and the coverage will stay in place until you decide to cancel it.