NEW YORK — A small but determined political organization in Detroit began to worry that its official symbol was a bit off-putting. With the group’s philosophy suddenly finding traction in the daily discourse, appearances mattered.

So in November, amid the country’s divisive presidential campaign, the National Socialist Movement, a leading neo-Nazi group, did away with its swastika. In its place, it chose a symbol from a pre-Roman alphabet that was also adopted by the Nazis.

Jeff Schoep, the movement’s leader, said dispensing with the swastika was “an attempt to become more integrated and more mainstream.’’

America’s nationalists are undergoing a rebranding, as part of the so-called alternative right: a grab bag of far-right groups that share the belief that white identity has become endangered in an era of diversity and political correctness.

The deceptively benign phrase “alt-right’’ now peppers the national conversation, often in ways that play down its fundamental beliefs, which have long been considered intolerant and hateful.

The term’s recent prevalence corresponds with the rise of President-elect Donald Trump; alt-right leaders say his inflammatory statements and Twitter habits in the campaign energized, even validated, their movement.

The movement is also acutely image-conscious, seeing the burning crosses, swastikas and language of yesteryear as impediments to recruitment.

Its adherents talk of “getting red-pilled,’’ a reference to the movie “The Matrix,’’ in which the protagonist ingests a tablet that melts away artifice to reveal the truth. New, coded slurs have emerged. Fewer pointed hoods, more khaki pants.

The alt-right movement is hardly monolithic. The factions within its ranks can differ on any number of subjects: white supremacy versus white nationalism, for example, or the vexing Jewish Question.

Andrew Anglin, the founder of the neo-Nazi, alt-right website The Daily Stormer, described the current moment in a recent essay as “a reboot of the White Nationalist movement’’ — one infused with youthful energy.

The foot soldiers of the movement are not old white supremacists marching under a new banner, Anglin explained, but a mostly younger generation drawn from various online cultures, including conspiracy theorists and that misogynistic stratum of the Internet known as the “manosphere.’’

Then came Trump, whose opening gambit as a candidate included his promise to build a wall to keep out Mexican immigrants, whom he called rapists and criminals.

Trump went unscathed for engaging with Twitter users like WhiteGenocideTM, who listed his location as “Jewmerica’’ and used an image of the founder of the American Nazi Party as his Twitter profile’s photograph.

Trump brushed off his sharing of alt-right messages on social media as the sort of thing that just happens on Twitter. He also denied the existence of any alt-right movement.

“Nobody even knows what it is,’’ he told CNN in August. “This is a term that was just given that — frankly, there’s no alt-right or alt-left.’’