We booked our car hire as part of a fly drive and we had this exact situation with Budget when we arrived in Orlando. The booking was in my husband's name with me as an additional driver but they wouldn't accept my husband's credit card because it was Santander and they hadn't heard of it (don't get me started on that one even though it was a Visa) and the only other credit card we had was in my name which they wouldn't accept because the booking wasn't in my name. So, we had to change the booking into my name so they would accept my credit card even though I wasn't intending to drive much. My husband then drove out of the car park and drove virtually the whole holiday with me driving ocasionally.