Any sort of character concept that depends on witholding information from the other players is extremely difficult to do in a satisfying way.
The other players can easily not care about your mystery at all, making your secret just you and the dm making eyebrows at each other. Or they’ll care more than you want, and any sort of long-term intrigue goes out the window as the party drills into your character. Or hell, maybe they’ll be annoyed that you’re being so coy about your character, maybe they’ll find it shifty or frustrating or any of a dozen other things. And even if there’s the perfect level of investment and buy-in from everyone else, it still runs the risk of being a spotlight hog of a character.
So generally it’ll either have absolutely no impact, or it’ll derail the party.
Oh, and all of this goes for double if your secret is that you’re working against the party.