If someone buys a car and someone else pays for it who owns the car?

Usually, if you "buy" a car, you pay for it. If someone buys a car and gives it to you as a gift, that's different.

If someone agrees to pay for the car through a car loan, but you will drive the car and be responsible for maintenance, repairs and liability, the lender will usually require both names to be on the title. If somehow the lender was not informed about this arrangement, you may have a whole other problem, possibly involving fraud on the lender.

Ultimately, the person whose name is on the title owns the car.