I believe that most states titles go by the body but some go by the frame and others go by both. It would be worth your while to check at your local motor vehicle dept. prior to swapping.
I swapped the (rotten) frame out of my TJ and being that I already owned the Jeep had current plates and registration already, I didnt wanna stir things up.
I also put a 93 YJ body onto a 91 frame due to collision damage on the 93 and rust damage on the 91; I just used the 93 title to register it;
but I am watching this thread for other answers since I found a PERFECT Dodge Ramcharger body in the 'yard (some stupid A hole "clunkered" it; this truck is definitely no clunker) and I'm looking to buy a rusted hulk for the powertrain, frame and title. then just swap this body onto the donor frame with its title etc.
This would be teh reverse of what I'd done with the Jeeps; trying to go by the VIN of the frame instead of body.
It varies slightly by state but there are many similarities. Most states restrict changing any major component, IE the drivetrain, frame, or tub, that has VIN's affixed to them, requiring an inspection by the State Police or Highway Patrol afterwards to check all VIN's against all bills of sale.