Can a person have someone else put insurance

Technically, the insurance company doesn't care WHO is paying the insurance, only that it is paid, and they know who's operating the vehicle on a regular basis.

No need to hand over the registration to someone else.

I guess it depends on the insurance rule in your state. I would call an insurance agent and asked them if that is necessary.

I think that most states require that the owner of the vehicle take out the insurance...but that doesn't mean that someone else can't pay for it so it wouldn't hurt to ask someone if they could do that for you. As long as the premiums get paid the insurance companies don't care where the money comes from, but if the car is in your name so must the insurance on it be.