Try to select a name by lot. Each participant writes one or more variants of the name (depends on your quantity) on the same leaves, folds them, puts it in the bag. Then the man with closed eyes pulls the first available piece of paper, unfolds and reads aloud.
If you choose the title alone, use at name selection guidelines. First, what city and institution bound team? Perhaps this word will become a part of the name as already famous orchestras "Moscow virtuosos", the "Virtuosi of Moscow state pedagogical University," and so forth.
Write down the terms associated with the style and direction of your creativity. They, too, can become part of the title. Try to translate them into different languages, better – known to the whole team.
Analyze character traits, their own or all participants. Identify common similarities with the manners of some animal (cat, weasel, bear). Try to imagine yourself with this word, including translation into other languages.
Think of the contingent team: average age, gender. Call command feature, typical for members of this group. Feel free to use a dictionary, including Russian-Latin.
Collect the first letters of the names of the participants and place a few orders until you get a word or a surrogate. What you will like, and will become the name ofM.