Shipper
On a bill of lading, the shipper is the person or company that tenders the car. That is you, or whoever controls the car, not the carrier and not the broker who arranged the truck.
Shipper is the word on the paperwork for the person who hands over the car. 49 CFR 373.101 requires the name of the consignor and the name of the consignee. On a car shipment, the consignor is the person who tenders the car, which is the shipper. The consignee is the person who receives it. They can be the same human. They often are not: you book the job, and a buyer, a relative, or a dealer meets the truck.
What you are responsible for
The shipper confirms that the car is the car on the order, that it matches the operable or inoperable description, and that the condition notes are accurate before anyone signs. If you are not at pickup, the person who signs is acting for the shipper. Tell them to read the diagram, not only the price.
The carrier is not the shipper. A broker is not the shipper either, unless the broker owns the car. Mixing those words is how a damage argument starts with the wrong company.
How this differs from the company that sold you the quote
The company that took your order may be a broker. The company on the truck is the carrier. You remain the shipper. RideShipper is not the shipper, the carrier, or the broker, and it does not sign the bill of lading.