Party names don't mean a whole lot. For example; The modern Communist Party of China.
This is unequivocally true, and the Nazis kind of showed that themselves. Nationalist, yes. Socialist, depends on your definition. German, yes, if led by an Austrian. Workers, in it's own way, but not in the customary way. In all events, their name may have been accurate in the 20s - a nationalist party with socialist ideals - but by the mid 30s, it wasn't at all.
At least they didn't have the gall to include 'Democratic' or 'Liberal'.
Anyway, the Nazis were the original far-right party, in terms of non-Democratic, nationalistic populism.