In the prequels, the Jedi exist in the open and think that the Sith are extinct.
My idea is that instead, the public would be unaware of the existence of either, but the Jedi and Sith would be aware of each other’s existence, but wouldn’t know each other’s identities beyond aliases. The aliases used by Sith wouldn’t include “Darth” and there wouldn’t be a “Rule of Two”.