Registration of a car

I suppose you could come to some agreement with the seller to leave the car parked where it is until you get your papers in order.
You must get a HU drivers license within a one years time of living in HU.
Otherwise you are not suppose to be driving in HU.
You must also have insurance on the car before taking it out on the street so no way to drive it legally until you fix the paperwork.
If you have not moved away from the old address on your old card, then there shouldn't be a issue with the address for registration.
The paperwork in HU for driving, registration papers goes with the owners and not with the car.
Not 100% sure of what your asking about putting the car in someone else's name? Suppose you can do that but you can't drive without being covered yourself with insurance and driving paperwork.
We own a car, I have a 10 year visa, my husband has HU driving papers but mine are still only from the US.
Same address and all paid up with insurance but I do not dare even move the car down the street since I legally am not able to drive on the streets in HU.
If you want to roll the dice it is up to you.
I know people who drive in HU without having a proper HU license , one guy is HU and is blind in one eye, could never pass the test here.
Not sure if he has the car in his in-laws name or his though.
You must also be able to trust the person who name you register the car with.

Oh sorry reread the post, since you do have driving papers for HU then I would think if your address is still the same there should be no problem need insurance though.