Sounds a little odd as I'd expect there to be just one value everywhere in Analysis Workspace. Those "friendly name" values are being set by the TnT classification file, so an admin user can go to Admin > Classification Importer, export the TnT classification file and check what values there are in that file
If that file contains the new "Red to Green Button Test Jan 5, 2024" name and you still see the inconsistency in Analysis Workspace then I would suggest you raise a ticket with Customer Care