I haven't spent much time personally in Cali, but the places I have had to rent a car from I've never had a rental car plated in the same state I'm driving/renting it from

the rental car is obviously already going to be legal in the state (if not cali plated, then registration is probably via fleet registration or international registration plan (IRP), etc).

under no circumstance are you (the customer) going to be required to (or even able to) register the car you are renting.

i would not take car registration advice from a person asking about registering someone else's car at the dmv.