I have seen a number of comments about the movement calling themselves the "alt-right"; these comments argue we should not accept these peoples' name for their movement, but rather call them fascists, racists, national socialists, misogynists, and plain haters. An Internet activist has written a Google Chrome plug-in that renames "alt-right" to White Supremacy or neo-Nazi. The Associated Press has also updated their style guide to require quotes and a full definition whenever writers use the term "alt-right".
I sympathize with the impulse, but if we reject the name "alt right" we stand to lose potentially useful information. The name a person or a group gives themselves is always a "tell"; it gives away more about the people who take the name than they intend.
It's worth considering what "alt" means. Any group calling themselves "alt" announces themselves as a product of the Internet age, a set of connections forged on social media and its precursors. Beyond that, "alt" situates the group according to Internet nomenclature. The "alt" designation dates back to "usenet", an information distribution system that predates the World Wide Web. The designers of usenet divided the topics into hierarchies: "soc" for social discussions, "sci" for science related material, and "alt" as a space for carrying on discussions without moderation (in either sense of the word) and too often without responsibility. The participants of discussions in the "alt" usenet groups devised methods of making conflict on the net personal, forms of personal and professional attack participants in the so-called "gamergate" controversy would later engage in.
The name "alt-right" thus claims an association with Internet discourse defined by its lack of restraint and lack of any form of intellectual rigour. If multiple surveys of ordinary Trump voters have accurately measured their thinking, this exposes a critical disconnect between the extremists who call themselves the "alt-right" and the mass of people whose votes put Donald Trump in power. If average Trump voters want authority to keep them safe, and his most extreme supporters have taken a name indicating a refusal to accept either authority or accountability, that indicates a fissure in Donald Trump's coalition, which we can hope will end up isolating the racists and misogynists of the "alt-right".