My mother also had a period of rejecting/fixating on her clothing and while it's a bit better, it's still an issue.
She had three walk-in closets stuffed with clothing but also piles and piles of clothes all over her home. Despite this, she would only wear about two pairs of trousers and five tops, over and over (and of course she was not washing them or herself).
Now she is in a care home, and she seems to need to have a certain amount of clothing (a baseline, if you will) to feel comfortable/reassured. This is also true of snack food, toilet rolls, and Kleenex.
I finally figured out that part of the problem was that if she can't see the clothing (she leaves the closet doors open and the care home doesn't mind, thank goodness), then at times, it does not exist for her. So you might try leaving the wardrobe open, removing the doors, or replacing it with just a rod/rack for hanging clothes on.
My mother will often reject new items of clothing if I tell her they are new, but if I bring them in a plastic carrier bag, she will often say, what is in the bag? Oh, look, it's my (top/trousers/whatever), I wondered where I had put that, and I will say something like, it was in the wash, Mum, here you go.
Name tags or marking clothes may or may not work. My mother was initially offended by the markings but now can no longer seem to see them. She can, however, see the sizes marked in the clothing, at least some of the time. You never know, with dementia.
I hope you will find something that works!