@nicholas @feld

None that I have much direct experience with, because not enough geek/privacy-conscious friends willing to use them. However at face value, Threema, SimpleX, DeltaChat ... none of those have any requirement to provide personally identifying information.

https://simplex.chat/
https://threema.ch/en
https://delta.chat/en/

I would ideally include XMPP+OMEMO too, but the client-side cross-platform support is absolute garbage, and the crypto is quite outdated. Also it only protects the message content, not the metadata. But at least it's been around forever, is based on open standards, and has formed the backbone of many other chat platforms over it's history. So still worth an honourable mention, even if not a recommendation.