I didn't mean (though it certainly sounded that way) that it's necessary for the reader to know your gender. Looking back, in fact, I realize that I weakened my position by even mentioning it (especially in the vague, imprecise way that I did).

I brought up gender because it was confusing (and I, along with other readers here, felt misled) when you – very casually, I might add – mentioned you were engaged to the CEO, up until which point I'd been under the false impression that you were a man.

So, to answer your question: no, you wouldn't have needed to inform the reader of your gender if you had an ambiguous name because what's really important here is not that you're a woman but that you're engaged to the CEO. Whether you're a man or a woman is irrelevant: all that is relevant is that you have a close personal history with the guy you're negotiating with, a fact which, again, completely skews the context of the article.