Associated Press issues guideline how to use the term "Alt-right" in articles:

[DetlefK]

https://blog.ap.org/behind-the-news/writing-about-the-alt-right

Usage

“Alt-right” (quotation marks, hyphen and lower case) may be used in quotes or modified as in the “self-described” or “so-called alt-right” in stories discussing what the movement says about itself.

Avoid using the term generically and without definition, however, because it is not well known and the term may exist primarily as a public-relations device to make its supporters’ actual beliefs less clear and more acceptable to a broader audience. In the past we have called such beliefs racist, neo-Nazi or white supremacist.

Boilerplate

Again, whenever “alt-right” is used in a story, be sure to include a definition: “an offshoot of conservatism mixing racism, white nationalism and populism,” or, more simply, “a white nationalist movement.”

...

We should not limit ourselves to letting such groups define themselves, and instead should report their actions, associations, history and positions to reveal their actual beliefs and philosophy, as well as how others see them.