This could be implemented as a toggle, I like the idea. The only thing about this is that we would still store the user ID on our backend, for obvious reasons of keeping it all and for blacklisting. I'd have to think it over and how it would work with both our backend as well as making sure the user is completely anonymous etc, but I'm liking the idea of it.
The only thing that i would add, if we do have a way of blacklisting users from the anonymous feature, is it would warn the user before they contact, do you think this would be a good idea? I think it would be jarrying to message in, expecting to be anonymous and suddenly it showing your username.