If your name is on a joint car loan, then you will need the other person to get a new loan on their own to pay off the existing loan. You could also ask the lender if they will allow the joint owner to assume the loan on their own and remove your name. However, this will probably require the lender to run a new credit check on the joint owner, and your name will not be removed if the other person cannot get approved for the loan on their own.