Carrier
The carrier is the company whose truck moves the car. A broker may have sold you the job, but the carrier is the company that takes possession, signs the bill of lading, and hauls the vehicle.
The carrier is the motor carrier: the company authorized to transport the car. Its driver loads the vehicle, its insurance filing is the one that matters for public liability, and its name should be on the bill of lading.
Why the names may not match
People often book with a broker, then meet a driver they have never heard of. That can be a normal handoff. It is a problem when nobody will give you the carrier's USDOT or MC number, when that number does not match the legal name, or when the price changes because a different company showed up. Ask for the carrier's docket before you hand over the keys. Look it up yourself. A screenshot from the broker is not the lookup.
FMCSA requires interstate for-hire carriers to hold operating authority in addition to a USDOT number. Private fleets that haul only their own cars are a different case. The company that advertised to you may hold broker authority only. Broker authority does not put that company behind the wheel.
How a carrier differs from a broker
The broker arranges. The carrier possesses the car and moves it. RideShipper is neither. It does not assign the truck or sign the paperwork. If you want the truck, hire the carrier, or hire a broker and then confirm which carrier that broker assigned.