Is there any unique information that I have to obtain from a Uber driver?

If you are a passenger in the Uber vehicle, you will likely have the name of the driver and the basic data required to identify the driver and timely report same to Uber and their insurance carrier. Obtain the basic information that you would in any accident. If you were not a passenger in the Uber car which was involved in the accident, obtain the license plate number and if possible any other identifying data indicating that the vehicle was a Uber vehicle.