Iman /iman/ [2 sylls.] as a boys' name (also used as girls' name Iman) is of Hebrew origin, and the name Iman means God is with us. Iman is a version of Immanuel (Hebrew): transcription of Emmanuel. Compare last name Oman.
Simple assault or battery is the least serious form of assault or battery, usually involves minor injury or a limited threat of violence, and is a misdemeanor.
Then you have a misdemeanor battery but the injuries upgrade it to a Felony Battery. Aggravated Battery (without a weapon) is a lot like Felony Battery. There is a battery and there is great bodily harm. The difference is that with an Aggravated Battery there is the Intent to cause the great bodily harm. So again with your hypothetical, if you punched the cashier and specifically intended to cause the broken nose/broken tooth/scar, and actually caused it, then there is an Aggravated Battery.