Who has the car
Who has the car means which company is responsible once the keys move. The broker arranged the load, the carrier holds the authority and the truck, and the driver is a person. Get all three names in writing before pickup.
Before pickup day, you should be able to write three lines. The broker, if there is one, is the company that sold the order and may have taken a fee. The carrier is the company whose docket and bill of lading cover the haul. The driver is the person who arrives, working under that carrier's authority. If you can only fill in one line, you are not ready to hand over the keys.
Where each name should appear
The broker is on the order confirmation. The carrier is on the dispatch sheet, with an MC or USDOT number you looked up yourself. The driver is a name and a phone on that same sheet, and the name on the door should trace back to the carrier. The bill of lading at the curb should repeat the carrier and the VIN.
Why the question matters
Damage claims, refunds, and a demand for more money all go to a named party. "The company" is not a name. RideShipper is not holding the car. If the answer is missing, delay the pickup. A written answer you checked is the whole point of the question.