Hit in the back of the head with a foam dodgeball 12 hours ago. no loss of consciousness. no severe headache. brain damage likely?

Very unlikely: I am sure you will be fine. That is the danger in dodgeball i guess.

Not likely: Healthy 22 yr usually has a pretty hard-head. It has been 12 hours and you don't really have any concerning symptoms and so significant brain injury is highly highly unlikely. If u were 72 it would be a different story because of a possibility of a very slow bleed. So, just be careful playing sports/protect your head, otherwise you are lucky this episode. Good luck.