Name Toss
One of the most common games used in the process of making introductions is a game of catch. Players sit in a circle with one person holding the ball. The ball is passed around the circle clockwise as each person states his name. Once that round is complete, players must toss the ball across the circle to another player, stating that person's name. In the beginning, the names may repeat, but as different people who remembered different names get a chance with the ball, most, if not all, of the names will be used over and over again.
Zoo Names
Another game that can help with names is one where players again sit in the circle. The first volunteer states his name and follows it with the name of an animal that starts with the same first letter as his name. For example, "Danny the Dinosaur." The person sitting to Danny's left must repeat "Danny the Dinosaur" and then add her name and animal, "Amy the Alligator." The third person must state the names of the two that went before him and add his name and animal. Proceed all the way around the circle. By the end of the game, everyone, regardless of how well they performed, will have a good idea of what everyone else's name is. They may, by accident, recall that person by his animal as well.
Truth or Lie
Another game you can play with a new group of people is called "Truth or Lie." This game offers a little information about a person as well as what his name is. Have each person go around the room and state his name and two facts about himself. One is true the other is false. Everyone else must guess which fact is the lie and which is not. By the end of the game, the interaction will help everyone remember a little something about each other in addition to their name.