Shiho Ide, a participant in my Tokyo English for Activists class, came up with this nice way to do introductions.
Standing in a circle.
The first participant introduces herself, saying her name and what she would like others to call her. She then chooses another person who must ask her a question, any question. After the first person answers the question, the second person repeats the process.
Comment
What made this useful was the nice way it followed on Me --> You, with people recognizing each other as individuals as they became recognized by the group. The freedom to ask any question was also a relief (rather than ask the standard, "what do you do?" "where are you from?" "what is your favorite color?") and let us see glimpses of the group's personality and interests. Likewise, people felt free to ask follow-up questions.