It’s not like there are people checking for immortals, I think it would be flagged by a dmv employee or something when they dont believe a clear 21 year old is actually 150. Let’s assume it’s current day im caught and not bring speculation on what the US is like in the year 2139 is like.
So, what I would likely do, is go to a country with somewhat easy-to-bribe officials, get a new identity made there; Then get a degree as an OBGYN and slip false names into their system.
you can then re immigrate to wherever, get a somewhat corrupt doctor to keep the “family” running so you get new identities that don’t involve taking over actual people’s identities.
depending on how careful you want to get, you’d have to then generate fake histories with residences, and eventually careers, but given the ability to compound inordinate wealth; it wouldn’t be too hard.