As long as your motor vehicle is not parked on the street or in a public parking lot it does not need to be registered.
If you want to cover it it's up to you but it makes no difference if it is in your own driveway.
Some towns and villages have some strange parking ordinances that may cause you a problem but these ordinances usually deal with parking commercial vehicles in driveways.
Since I don't know where you live it's impossible to say for sure. Check with your local municipality.