I used to work for Avis. We--and Hertz, Budget, National, and Dollar--all required that our renters either be 25 or older, or active duty military with ID, and that they have a credit card--not a debit card--issued in their own name.
The reason was that younger drivers accounted for an extraordinarily high amount of damage to our vehicles, like 80% of all damage, from accidents to abandoning it someplace it was stolen to car fires.
The only time I ever saw my manager make an exception was a customer put down about half the value of the rental vehicle in cash as an additional deposit. He was 23.
So if the policies have not loosened, not only will you not be able to rent without a credit card in your name, but you won't be able to rent based on your age.
This would be limited to the national chains. It's possible a regional or local car rental place would rent to you.