What happens to the car holder if the car was paid for with a credit card, card holder wants their name off?

Much of what you say doesn't make a lot of sense but basically if both names are shown on the car title and there is no lien holder then you are equal co-owners of the vehicle - regardless of the balance of payments made toward the purchase. If two credit cards were used to make the purchase then the respective owners of the cards are responsible for payment of the debt incurred on their card regardless of the status of the legal title to the vehicle. Provided there is not a lien holder, title to the vehicle can be transferred to one of you by the other as either a gift or with consideration (i.e. money payment) by following the laws of your state for such transactions. If there is a promissory note involved then it would be considered by the courts on its own merits and would not in any way govern the ownership of the vehicle.