the group name is whatever you want it to be.
when using the Cirrus service, you're sharing the service and the group namespace with all of the other developers using the service. so you should choose your group name to be probably unique. one way to do that is to include your domain in the group name, like a namespace. for example, if my domain was example.com and i wanted to further subdivide it (maybe my email address is "email@example.com", and i wrote an application called "myapp"), i'd do something like:
var gs:GroupSpecifier = new GroupSpecifier("com.example.mike.myapp/somegroup1234");
but there's no restriction. it can be any string, in any language, and of any length.
GroupSpecifier.makeUnique() adds a globally unique cryptographically pseudorandom token to the groupspec, making the groupspec globally unique and impossible to guess. the only way to join a group that's been made unique like that is to obtain the groupspec from the party that created it or that has already so obtained it.