How to transition conversation from a public forum to an encrypted messenger without divulging personal contact information?

To my limited understanding your session id is a unique identifier like a phone number or bitcoin wallet. Aside of the hurdle of getting someone to download yet another app, the unique identifier still stands to be connected back to you. (Especially if posted publicly.) I’m looking for an OTP style session ID. I don’t want multiple forum alias tied together with a central session ID.

I realize the scenario is a bit obscure.
-P