Joybell, I think we call that a Blackboard Concert here, same principal but with the names on a blackboard. But that is 'organised' and the most memorable singarounds I've attended were less formal.
Politeness and respect are required in an informal situation, and sometimes a known 'organiser' can use his/her Mana to restrain the over-enthusiastic, which is really the only problem. The excessively shy must bring a friend who knows they sing.