This is called in law a bailment.
"Putnam's Handy Law Book for the Layman"
Albert Sidney Bolles
At the expiration of the bailment he must deliver the machine to the owner or person authorized by him to receive it, and is liable if neglecting or refusing.
"Putnam's Handy Law Book for the Layman"
Albert Sidney Bolles
Lastly, if the car is driven by the garageman's servant while the bailment continues, the bailee, and not the owner, is responsible for any injury done to a third person by the servant's negligence.
"Putnam's Handy Law Book for the Layman"
Albert Sidney Bolles