I think there is some interesting stuff to write about for this topic.
For a person who embraces a facade, take a look at Iago. His public persona never matches his true private intentions, where he selfishly simply wants to rise to power by shaming Othello, and using other people such as Roderigo and Cassio to his own advantages. Just take a look at his nickname - "Honest Iago", the most blatantly ironic thing someone could call him, yet it is repeated many times throughout the play by many characters.
Even Othello has moments in the play himself where his private self remains different from the public - just take a look at when he begins to get suspicious of Desdemona from Iago's lies, yet when he first hears this, he attempts to not know about it, despite Desdemona noticing that Othello seems to have been acting stranger.
If the question is about both public and private facades, you could also elaborate on another argument. Is the way that the characters present themselves in their most private moments, such as in their soliloquies, really truthful, and really reflectant of their character and intentions? Or are they simultaneously trying to mask something from the audience, as they do from other characters as well? Iago sort of embodies this by later affirming to the audience that his intention to destroy Othello's life has moral grounds behind it, claiming it is revenge for Othello apparently sleeping with Iago's wife Emilia, and I believe later also stating it is simply his nature to get mad and jealous, thus Iago is not responsible for ruining has life (though I can't remember which quote this could be).
I hope this helped. I loved studying Othello, it was probably my favourite Shakespeare play to study in school. Good luck!
