Not on the avatar, on the username.
My particular use case:
We have teams (groups) responsible for different areas of a workshop. Some people are members of multiple teams. It’s good to know what authority a person holds when you’re talking to them. “Ah, I’d better listen to what Jane says about the oscilloscope; she’s got a little lightning bolt by her name which means she’s an electronics technician”
EDIT: My html bodging made the user info bits display on new lines. ignore that 