Oh, you have no idea the amount of consternation and embarrassment we have over the naming. Our leaders are sort of gay, I have to admit. We've continued to use "alt right" because the other name they came up with was "Identitarian." Yeah, they're gay. (Sometimes literally, in the case of Jack Donovan.)
The root of the problem is that, in actuality, we're just the right-wing, period. The true right-wing. Cuckservatism co-opted "the Right" in the 50s/60s in America (and its appendage, Canada). But in most Western countries, they would recognize Trump as a far-right candidate. For example, in France, Trump would fit right in with the far-right National Front party of Marine Le Pen. All the European countries have a similar far-right party that is anti-immigration and anti-globalization.
As I've said before, the other Republican candidates are more "conservative" than Trump. But Trump is more right-wing than them. We really should just call ourselves "right-wingers" but in this country, people will think we want to lower the capital gains tax, lol, instead of deporting Mexicans and Muslims.