I can only state what the law requires here, in DE. It requires you to know that (but admittedly you're usually going to get a picture with the first request for information, so it's mostly a matter of "Hey Joe, you've got a new mugshot!" and passing it to the right one of five) and has ways to "motivate" you if you fail this in a harsh case or repeatedly.

Which is fair in my book: You own the car, you are responsible for it. You're not on the hook for offenses that you didn't cause. But you were careless with your car if nobody steps forward after an incident.