At this time we are alerted that we have X amount of new inbox messages but we aren't aware who by at a glance. The suggestion is for a popup of the avatar of the person who sent that message or started the latest message so we have some idea who sent it.
If this suggestion has been made feel free to merge the thread.
Edit: Maybe the person can select an option whether to be notified by alert balloon or via members avatar. Options are always better.