I assign student laboratory groups randomly in the classroom, so they change with every lab.
I use playing cards for this, so I have made a bunch of group-sets. One of these per lab. However, each group name is the same, since I made one and cloned the group set.
I have run into two problems, however:
1. My students see the group names, and the groups set name, but they are not organized when they sign up for a group. So they have to scroll through many groups to sign up. It would be really nice if their group sets were organized like mine are, but that is simply a minor problem.
2. The students work together on spreadsheets, however if they try to collaborate using Google Docs they cannot just pick their group name, as there is no identifying characteristic. For example, if there are 5 labs, each with a group "aces" they all show up but with no identifying name. So, it is impossible to know which lab the group corresponds to.