I don't know if an icon is attached to a user group, but if it is, the text should display for that icon's user group.
That way we can create a user group "Icon: Checkmark" with no permissions and add a checkmark icon with the text (that's seen on hover) as "ABC".
Then, if we want user A to...
It would be nice if the icon next to the username can mimick XF's overlay and display custom text assigned to each icon.
This is like most social media sites (excluding Twitter, as I believe they coined the checkmark) for various tasks.