From the AP’s blog on how to use ‘alt-right’:

“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.