That's easy to do on Nostr with secure messaging protocols like double ratchet and probably MLS. Just add "create anonymous chat" in the UI.
It's just that relays can probably figure out who you are if you also make other Nostr requests. Maybe need a different client and relays if you want to avoid that.
SimpleX has no user identitifiers of any kind. Not just no publicly exposed identities. Given the nature of nostr, I'm not sure truly identity-free messaging is possible.
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