As you may have noticed already, to meet the expectations of users, we have changed the meaning of the formerly-labeled "private" button in the lobby.
As of now, this button is labeled "Native" and allows you to switch to the non-English chat window.
In short: you can write in your native language, without disturbing people communicating in English. Messages written in this window are now visible in all lobbies (tournament, regular and training), but this could still change.