They don't particularly like socialism (unless it's for big business and billionaires), so we'll need to come up with a shorter, snappier name to hide that part. I just do not see that happening though...
Some Nazis who are averse to the word “socialist” have been replacing it with “traditionalist” (because, you know, that’s based, with tradwives and white-picket-fenced churches and all that). So, National Traditionalist American Workers’ Party could work
If you rearrange it to National American Workers' Traditionalist Party you can give it the acronym NAWT. Prononced as in "this party will definitely help American workers. NAWT!"