A man who does all of that, wears 'women's clothes', and adopts a 'woman's name', and still says he is a man, is weird
See I don't have a problem with men rejecting masculinity, as long as they admit their ongoing maleness
I'd go even further and say I am actively in favour of men rejecting their masculinity, while admitting their ongoing maleness.
And I'd especially like to move as far as possible from the idea of "women's clothes" and "men's clothes" anyway. I thought we were the ones that were beyond all that.
Possibly it's an age thing, for me. In my youth I knew straight men who wore skirts and painted their nails, and sure, some were wankers, but some were "oh, hey, we can get away with wearing skirts now, I like it". (I had a similar revelation about a decade ago about nail polish, which I had never worn. I was buying some for my sister, who likes it, and me and DS went OH WHAT IS THIS IT'S SO SHINY and I bought some for us and went mad with it. I don't wear it often, and I apply it with all the skill of a toddler fingerpainting, but it's PAINT and it goes on your NAILS, what's not to love?) On a slightly different axis, I've always known gay men, including plenty who do drag, and use she/her pronouns, and that's never until now been about claiming biological womanhood. (I know lots of women here really don't like drag, but I don't have a problem with it.)
So, yeah, there isn't any such thing as women's clothes. (Even if Eddie Fucking Izzard has changed his mind on this.)