I'll echo
@stitchfan18 's experience. When I once reserved a car through Costco for Alamo, I had put DH as primary driver. When we got to the counter to pick up the car, they had to change the name on the rental agreement to match the name on the card even though I was going to be an authorized driver (I have a CSR but he doesn't), i.e. the name on the card used for payment had to match the primary driver's name.
A couple years ago, I had an "accident" with a rental car (somebody scraped it with their car while it was in the valet's possession - the valet had the car keys - as I was checking in). Marriott wouldn't take responsibility for it because the valet guy wasn't physically
in the car when it happened.

It is a LONG PROCESS and rather confusing to deal with, and Chase's third party insurance handlers do things entirely online so it's hard to get questions answered. It eventually became an nothingburger when Alamo couldn't get its act together to provide me the paperwork for damages, and they closed out the claim. But it was hanging over my head the entire time and that was stressful. It made me especially mad since it wasn't even anything I did!
To anyone using UR points to pay for a car rental, I strongly recommend that you select payment in a way that puts a nominal amount on your CSP/CSR in order for that to show up on your cc statement. You need to provide proof of payment on the CSP/CSR for coverage and having it show up on a statement is helpful.