Luffy said to Yamato she can’t be Oden, to which she responded : "Then do it yourself !". So the way I see it, it’s not that Yamato just wants to be Oden because she admires him, she assumed his identity because she sees this as a role she has to fulfill until the country is free and Wano borders are open. "Kozuki Oden" is like an unofficial title in her eyes. That’s why she doesn’t really seem to see herself as a man and simply puts on a mask instead of literally becoming a man.
Maybe that was already obvious for everyone but it’s an interesting point to raise. It means she’ll probably stop pretending to be Oden after Kaido’s fall. I found this relieving because I wouldn’t like her to keep doing that, especially if she joins the crew. Be your own person.