Right now, the only place that states the Group Name of a Game Session is on the List views (Public, Group or My Games lists). And even that is only the shortened form of the Group Name and it's in small letters under the user's avatar. If you go into a Game Session page, as to see the individual players or the session chat, there is nothing to indicate what Group it's under.

I would suggest:
- Making the Group Name more noticeable on the List views
- Adding the Group Name to the Session view