i looking this as teacher..
yes it doesn't give any grouping name..
when i tick "available for group members only" all student can see the assignment even they are in the different grouping
Have you read groupings documentation ?
After ticking "available for group members only", you should be able to select a grouping (to restrict to). Then, when looking at all groupings in the course, you should see 1 in the activity column for this grouping.
If it's not the case, you've perhaps discovered a bug...