I was recently in a group of graduate students, and the facilitator started by having everyone introduce themselves to the group. She instructed us to think about our name, and tell the group a story about your name. It could be how you "got" your name, who named you what and why, or even how your name may have had a positive or negative influence in your life or in the life of someone closely related.
I think this is a powerful way to begin a group. It gives immediate insight to the leader regarding the students, gives each student an opportunity to open up and process, or to listen to another student "work" and reveal something personal that they will be able to remember about their fellow student. It is amazing how much some people will reveal about themselves simply by talking about your name.
(This exercise is EXCELLENT - especially as a way for students to introduce themselves. It helps a great deal in remembering everyone's name - J.S.)