I'm being pretty loose with terminology here. I don't call them names or anything, but I make sure punishments are directly related to how they mistreat others.

For example, if my kid is bullying others at the park, I remove them from the park until they're ready to apologize or it's time to go home, and I don't mind embarrassing them in front of their friends. Playing at the park is a privilege, and I'm happy to revoke that. That said, sometimes my SO will go overboard on punishments, and I'll step in to protect them if that happens (and they do the same for me). If they are misusing something to bully others (e.g. their bike), I'll take it away until they apologize.

There's always a discussion about why the behavior wasn't acceptable, how they can make it right, and what the consequences are. And every time we make it clear that we love them, it's just that specific behavior that's the issue.

It has worked pretty well so far.