The person who is named in the title is the only person who can register the vehicle.
You have to have the title, vehicle inspection forms , and proof of insurance.
If two names appear on the title and / or between the names , only one person has to come in.
If two names are on the title with and between them, both people that come in.
Clarify this by calling your DMV within their county. There will be a charge, I think ( in my state ) there is a renewal cost 10 dollars plus the cost of the new label.
That may depend entirely on state law. Add more information about your question , which specifies how much of the world is in :)
Here in Ohio , only the person whose name in the title tags can be purchased for the car.
PS Your father is screwed up . While you are paying all the money in this car , the rating of its parent credit is increasing. If you are just starting out in life , it is necessary to increase the credit to him. I know it was not your question, but I thought you should know.
The difference is tat if he owned the car you have to pay more money for insurance. This is because you are younger, and especially if you have a few years of driving.
So using the name of his father gives him a better deal because they have a better credit score than you.
The above mentioned person must use his name to build your credit. You can do that , but be willing to pay more money. Talk to your insurance if you get no credit for pay , as both names are on it.