How do I change the Group Trust Level @mention name

I guess that’s too short. If I were you, I would verify the name by entering it in the name field of the dialog to create a new group. There, you can see error messages related to group names the site text page doesn’t check for.

To check if a customization was done, CSS safe mode is very helpful as it disables all frontend customizations. But showing a different name than what is in the database might make it difficult to message or @mention the group.