Doesn't this burden the dealership's service revenue? They have to pay to maintain this fleet of rentals, which is going to be resource pressure for their service departments.
(disclaimer: I work in automotive, and very closely with dealers)
One thing is leaving information about the car and the dealership in the vehicle + providing dealer contact info in case the person wants to reach out to the dealer. Do you have any other ideas?
Dealerships live and breathe leads. People renting cars definitely do not want to be sales leads for dealerships. So I think this may be a pothole along your way to the success I hope you achieve. :)