Short of that, get rid of anonymous profiles completely. As far as the reason being some people would be afraid to ask embarrassing questions. That's ridiculous. You don't have to use your real name or your photo. So you're still anonymous. But it gives the user the choice who they will communicate with.
There is already something you can select to do that.
But I know sometimes anonymous users can be annoying or say something rude that's usually the reason why they do it...
But that's not always the case sometimes its do to embarrassment or other reasons. Just because they're anonymous doesn't mean that there reason is any less important helpful or meaningful as someones that isn't.