When you return the vehicle counter rep will ask if you "want to keep/put charges on same card?". You can say "no" and give them another card to swipe including a debit card.

IIRC the rationale behind not allowing changes of CC other than what is in profile and the matching name requirements is to combat fraud. People can, have (and apparently still do) rent vehicles with stolen CC's and or those created via ID theft. When this happens while National can place the original hold, often when they go back to actually charge the card they cannot. That and or awhile later the charges are reversed for fraudulent activity.

Have stood inline/at counter and watched as a counter rep tried to process a reservation and each time card comes up "declined". The would be renter simply pulls out another and says "try this one..." At some point you have to wonder if this person is just maxed out, or trying to run game.

Believe it or not many years ago you *could* make a reservation and pick-up a vehicle from National with a debit card. IIRC the problem was with Visa and MasterCard issued cards that the system couldn't differentiate between "credit" or "debit". Things have since been tightened up.