As to the second half of your argument, you keep saying this, but you are missing the point,
The name a woman is born with is her name. It is equally as valid as the name a man is born with.
So if there is a brother and a sister who both have their dad’s name from birth, it is equally their name for as long as they decide to keep that name.
But I’m not talking about that. I’m not talking about ownership.
In the case of the sister and the brother, both names are patriarchal - ie acquired by default from a man. Neither of them had any choice, but it is what it is.
They can decide to own that name, or change it by marriage or deed poll or whatever. But what they can’t do, is argue it didn’t come from the father and is therefore patriarchal.
This argument that we don’t know whether women passed the name on somewhere down the line is nonsense really because we all know full well that the patriarchal naming tradition has been the default for centuries in this country. Yes there might be the odd woman who passed on her name in 1830 or whatever, but the further you go back, the more this will be the exception. And if it was the case that women’s names are equally default as men’s, we wouldn’t be having this conversation at all.
But anyway, just believe what you want to believe. It doesn’t matter as long as your happy.