Moving Name is a good exercise to start off with the group, especially if there are many new members, not familiar with rules of the game and with other group members.
Organize the group into a circle. Have each person step in the circle, and say the name, accompanying the name with some kind of movement which is associated with the name by the presenter. The group repeats both the name and the movement of each person until the circle is complete.
The more complex variation would be to add 1 descriptive characteristic to the name (for example, Shy Dolly, or Relaxed Fred).