Which doesn't address my point. What has happened to give anyone the impression that Supergirl HAS a dual identity? Suddenly, everyone is dying to know, but with her face exposed, there's nothing to imply she's hiding anything. Why would people wonder who you are if they can see your face? It's an implication of a mask, but she doesn't have a mask, gives the impression she's not hiding.
I understand that we know she has an alternate life, but why would anyone in-universe? I'll just ignore that it's silly that no one can figure it out, since they've seen both Kara and Supergirl's faces, that's just a conceit you have to accept for the story.
In this case, the phrase "dual identities" means that Kara Danvers and Supergirl are both who Kara Zor-El is .
In other words, Kara Danvers is not a persona designed to "cover up" the fact that she is Supergirl, and the only reason she has not made it public knowledge that she is both Kara and Supergirl is because she wants to be able to have some semblance of a private life.
What Baker, as I understand things, wanted her to do is willingly give up her ability to have a private life by publicly disclosing the fact that she is both Kara Danvers AND Supergirl.