Using a card in your name at the Avis desk shouldn’t be problem. I have had a few where I’ve been first on the booking but used my partners card and vice versa.
No direct experience but just switching the names over I imagine would be possible. What the desk cares about more than anything is the voucher amount matching up with the hire. That said if you have the extra driver and use your card I don’t see it makes a great deal of difference who is named on the agreement.