Spoilers for Season 2 finale here.
In the end, Starfleet classifies Michael Burnham's very existence and forbids any discussion of her in a (to me) forced way to correlate with the rest of Star Trek canon.
However, even if Starfleet officers all vow never to speak of her, the fact is everyone knows her. Season 1 showed that most of Starfleet blamed her for the Klingon War. Even Kirk, McCoy ,Scotty, etc. (who would be junior officers at this time probably) would have heard of her. Yes, they all would vow not to speak of her, but honestly wouldn't this just cause uncomfortable silences around Spock instead of, you know, people genuinely forgetting her?
Even if all Starfleet personnel eventually adapt to not speaking of Burnham and learn to act normally about the massive coverup around one of the Federation's most infamous figures, nothing is stopping the Klingons from screaming about her every chance they get. Kor should be challenging Spock to a duel upon learning of his identity in Errand of Mercy to avenge the slayer of T'Kuvma, as should every Klingon Spock encounters across his life (and there are a lot).
Thoughts?