i would ALWAYS recommend reporting it to the police & getting them on the scene no matter how small the RTC, as details can always change. my dad had a similar situation where there was minor cosmetic damage and there was one lad in the other vehicle but then a few weeks later he got a letter from the insurers saying that there were 5 people in the other car and that they are blaming him for cutting them up then slamming on in a "crash for cash" style thing and he had to fight for a long time to prove that wasn't the case but without photographs and a police report etc then he couldn't prove anything and i think he got swizzed.
Insurers only need to be notified if you wish to claim (they like to count informing them as a claim even if you just inform them so i'd avoid that until absolutely necessary, then if they say why then just say you forgot) but i would DEFINITELY have gotten the police on scene to make sure everyone is open and honest and who they say they are and so details and the number people involved don't magically change later. I would also have taken pictures of everything and everyone including taking photos of their ID because all you have is a name (which you aren't able to verify) and a reg plate which the car could have been stolen or the driver uninsured and their name could magically change later to the real person who owns/it's insured under.
also injuries such as whiplash can appear later. Story time; I had a crash just over a year ago on the M53 where the car in front of me slammed on and hit the barrier and i hit the brakes and turned away but still hit him at about 50 and my car flipped and rolled and ended up upside down, i was able to crawl out with only very minor cuts (the car had 7 airbags which saved my life) and i even went into work the day after but still had a doctors appt at my GP just for a check-up and i was signed off for 3 weeks, it took about 4 days for whiplash to kick in, it just kind of happened one day/overnight and my back and neck and shoulders just felt like they were frozen and were agony to move, but for the 3-4 days after the crash i was fine and able to walk, not huge distances but the same gait and pace as usual, and then one evening/night it all just hit me & my body and i was suffering from whiplash for a couple of weeks and only about 2-3 days before i went back to work did it ease off. I still get flashbacks and sleepless nights even now but no physical effects.
so ultimately my advice would be; yes always get police on scene no matter how minor the accident & injuries can also be delayed so you may need to claim for them on insurance.
sorry for the long post.