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.