Yes and thats the same process. You really need a learning annex in hermeneutics.
look m8, whatever Adam called it, that was its name. Adam called her Woman. That is her name.
Do you deny that?
That's what scripture says. that's the context and the literal linguistic record.
Throughout the narrative she's called ha-ishi just like ha-adam. It's her name. Definite article.
You have no legitimate argument.