My internal thought of being lesbian is someone who has feminine trait(s) who is interested in others with feminine trait(s). But like almost everything else in this world, there are cases where this doesn't exactly fit. All you can do is accept that words are generally intuitive but can always have edge cases where you would least expect. So, I'm not sure I agree with the premise but hey, do what makes you feel better.
Oh and the part about Voldemort's mom using a male pseudonym was on point.
The problem is that it's necessary to update a birth certificate if you change your name. So, a birth certificate is a record of your history but is mutable. This really just boils down to the question of why would one's government need a record of their sex?