One of the easiest games is to have everyone sit in a circle and introduce themselves, and then give themselves a nickname. This can be a nickname they already have, or one they've just made up. This is a fun activity, and it has the added bonus of deflating potential bullies giving kids their own inappropriate nicknames.
Sociometric games allow the kids to find similar things about each other while learning names and interests. Tell the kids to find someone else in the class that has had the same breakfast as them, has the same favorite color, has a different religion, etc. This will turn into a mini scavenger hunt that helps with name learning.
Get a hacky sack or rubber ball. Say your name, then throw the ball to a child. The child says, "Thank you, Ms. Smith," then says his or her own name. The child then throws the ball to someone else, who repeats the exercise by saying thank you to the child, repeating the child's name, and then stating his or her own name.
Have each kid describe themselves by using the first letter of their name. For example, "My name is Peter, I eat pizza, I like Pez and my favorite animal is a penguin."