It's SOP for rental firms to zerox the renter's photo I.D. and require at least that he/she sign the rental agreement, if not fill in at least some parts of it. If the renter is from elsewhere, they also usually obtain his/her (alleged) local address and phone number for the period of the rental. If a credit card is used instead of cash, the rental agency also has that document. Many rental firms also now have time stamping security camera's video taping the rental office interior around the clock.
At least one that I know of won't take cash unless they can find someone to vouch for the renter, and it can't be someone standing right there. I once met my brother in law at the airport when he flew in for a job interview, and I had just flow back into town, after having gotten a ride to the airport, that is I didn't have my own car there. They wouldn't rent him a vehicle for cash, and my standing right there vouching for him, with my own ID(s) wasn't good enough for them. He had no credit cards as he was coming off a bad bought of credit card misuse and was trying to get well, which he eventually did.