I've been following the TV-show "Lucifer", a show about The Devil leaving Hell and opening a nightclub i LA. Here he starts working with a detective.
He goes by the name "Lucifer Morningstar", which can hardly be called a "secret identity" - the first being one of the Devil's most common aliases and the second referring to the story of his fall in the Bible.
Further more, he frequently and freely volunteers that he is indeed The Devil. To the detective he works with... to his therapist (well, he is in LA)... and to several others. So his identity is hardly a secret.
The problem of course, is that nobody actually believes him - even if he is telling the truth. For example, his therapist believes he's talking in metaphors, and find it easiest to just go along with his obvious "delusions".
https://www.youtube.com/watch?v=H0UHQ-JHHF8 (His wings been stolen)
So is there a good word/phrase for a "secret identity" that remains "secret", not because you try to keep it hidden (you actually do rather the opposite), but because nobody actually believes you - even though your telling the truth and is completely honest about who you really are.