On my site, the user profile page displays “leader” for me, since I have TL4. I think this should say “Trust Level 4” which is the text I use for that badge on my site. Same is true for other trust badges which seem to have some remnant of hardcoded names for trust badges.
Changing the badge has nothing to do with the actual trust level designations. The badges are just badges.
Then should @tobiaseigen consider using a plugin to change the built-in wording for each trust level? I know there was some hint to having a setting that changes the trust level names to match any suitable theme, but not yet implemented.
Sorry, maybe I need to clarify… on my site I changed the badge names from e.g. leader to e.g. Trust Level 4. We settled on this because it’s become terminology that we refer to frequently to explain to people in the community what’s going on - so calling a spade a spade is more transparent and clear.
If I had changed “leader” to “smurf” then it should show “smurf” on the user profile for users that achieved that badge. Right now it still shows “leader” which I think is a bug.
Badges have nothing to do with trust level naming, they are external add ons.
In the same way you could rename any badge to anything, etc.