Check with the actual authorities. While reflagging should be straight forward, if the new owner gets pulled over or when the boat leaves the USA, the paperwork won't match with what was shown on arrival.
It may be as simple as keeping a copy of the bill of sale
or old registration
info but better to ask first what will be accepted.
PS: Recent thread about a faux Viking long ship making the mistake of not asking the authorities. Lots of whining but they wound up paying for port captains because they failed to confirm it with the actual authorities.