Here's why I think it is more likely than not that the general public is aware of her true gender:

(1) If you look carefully, you will notice that her professional outfit is not entirely identical to that of other SKK staff members (her hanbok lacks the black stripe around the cuff).

(2) The fact that the "Blue Messenger" turned out to be female suggests that either (a) SKK was open to people of both genders at the end, which would be consistent with the dream of a more equal society; or (b) this woman heard of Yoon-hee's actions and decided to emulate them.

(3) If the SKK students who flocked to her side did not know of her true gender, some of them probably would have questioned their sexuality and possibly gone insane like Sun-joon did during the middle of the series.

(4) If the people at SKK were not aware of her true gender, what alternative explanation would TPTB come up with when she decides to take leave to have children?

I think that the reason why she is still referred to by her alias is because virtually all of her accomplishments associated with SKK have been under that name, so it would have taken too much effort to change all of the records to reflect her real name. Also, the reason for her professional outfit being masculine could simply be that this was one of the fields where there was not a significant distinction between male and female outfits (there are also some professions today where such is the case).