i'm not 100% sure, but you can get a "statement of facts" from a california dmv and claim the bike is in california and you want to register it there. that way you could use your own name.
it would be easier to use your son's address and you could still use your own name and he could send you the plate.
i've done similar things with cars when i lived in arizona. my car was originally registered in ca, and i wanted to keep the plates. this also side stepped the smog requirements. the dmv issued me my tags, sent them to me in az, and told me when i came back to ca i had ten days to get it smogged. i returned and never smogged the car. got pulled over for speeding a few times and the smog requirement never showed up on anything, and since i had the tags i was legit.
our bikes don't need smog or insurance, so it'd probably be easy to do the same thing.
if you use your son's name, i don't think he'd suffer any liability if you got in an accident. we're still treated like bicycles as far as accidents go. most likely a car is gonna hit you, and not the other way round.
if you plowed into a car, most likely their insurance would cover the damages to their car, and you'd get nothing. if you ran down a pedestrian, they'd have to sue you. and california lawyers would love that.
you can get insurance from companies that insure scooters and mopeds, but i don't know the extent of the coverage. i talked to a guy who insured whizzers (don't remember who so don't ask) and it was liability only for something crazy like 350 a year.
if you really want the status of a ca plate, i'd use your name and your son's address. the form is so basic they're not going to investigate (or care) where you actually live.
but, you might be creating more problems in your home state. depending on what your laws are, the cops may see and out of state vehicle and make you pay to comply with theirs. or they might just think you got it from a cereal box...
)