Unless you force people to stop being morons, then they'll carry on. In a case like this, the best option is to strip people of their individuality. In fact, I'm somewhat surprised that American schools don't have set uniforms to begin with.

Why is a uniform a punishment? If you're using that argument, then how different is it from a dress code in an office?

If people went to be arses and bully over fashion, then they can do it out of school and during the weekends.

And if uniforms are too much for a society dictated by names, then why not impose a dress code instead? Collared shirt/blouse, trousers or skirts, proper shoes, no branding allowed on any? It allows a certain degree of individuality that people seem to crave, but at the same time it solves the problem of 'fashion'. Oscar Wilde summed fashion up with his statement, "Fashion is a form of ugliness so intolerable, that we feel the need to change it every six months". If people wear clothes that are not branded, then not only does it cost less initially, but they don't need to change it every time some higher up decides the country needs a new look, and, more importantly, people can't look at you, decide thta you're wearing last weeks, out-of-season tack, and jump you for doing so.