User with no core role receives no label.
We have a team member whose sole function is handling comments. Using User Role Editor I made a custom role for her with just the permissions needed for her job.
If I also assign her a core role, the label badge is applied to her comments, but without a core role, it is not. I really don't need her to have any core roles though and it would be cleaner if I could not do so.
Are you sure, you've enabled the role in the "Display Comment Author Labels" section.
One of the roles she is assigned to was not checked, but the other role was.