It might be possible to have a plugin that would change the username in the user and topic and post models for anonymous users. It would be tricky to do it without breaking stuff. Also, quotes that mentioned users would either include their names or also need to be modified. If it’s worth $2000 to $5000 to you post in Marketplace.
You could hide stuff with css but it would still be there and that wouldn’t keep crawlers from seeing the names.
Given that your sso forces you to use names you consider private you’ve got a hard-to-solve problem.