You don’t have to set up groups within your forum to make this work. A forum can be a no groups forum and the icons will still show up.
All you have to do is
- enable Groups in your course settings
- create your group or groups
- upload icons that will display well as 20 x 20 pixel icons
- add users to the appropriate group or groups
Here is what students see when they hover over the icons to see what they are:
And here is what students will see if they click on the group icon: