Q What if the other guy refuses to report the claim to his insurance company?
If the at fault driver refuses to report the claim to his insurance company then you can report the claim. But you will, at least, need to know the name of the insurance company to which to make the report. Any other information is also helpful. It will be difficult to report the claim if you don’t even know the name of the at fault driver. That is why you probably always want to get the name of the other driver at the scene of the crash.