It doesn’t really matter if the schools do. And the bully’s parents are where they get it from. Kids don’t care about branding unless they’re instructed to do so by their families. I was bullied by a guy for years at school. Several adults tried to intervene, but it only stopped after I embedded a knife in the wall next to his head from across the room. Bullies like a reaction unless they think there’s a legitimate chance you’ll snap and murder them. Unfortunately that’s not advice you can pass to your children.