askchapo

i am pretty sure my understanding of this topic comes from Ishay Landa's The Apprentice's Sorcerer, a compelling read.

anyway...

Did they call themselves socialist just as branding?

yes. in the well-cited book above, Landa talks about the dangers of "taking fascists at their word" for their beliefs. the color red and use of the word "socialism" were specifically chosen and meant to disrupt and confound the emerging socialist movement by creating uncertainty and confusion among the frustrated, alienated working class gravitating towards mass action.

the fascists claimed to be socialist to angry workers in public, but were much more circumspect in their language when courting the elites and their capital formations, which they did extensively. these relationships and the fascists willingness to destroy trade unionists and suppress strikes made them the darlings of capital and they found eager partners in supplying slave labor to the capitalists.

there were probably some among the nazis that believed the movement was meant to elevate the common worker, but after the Night of the Long Knives the writing was on the wall and there would be no organizing among whatever was left of that faction after most vocal proponents had been liquidated.

by the time the nazis began their invasion, they enjoyed lots of support from aristocrats and business leaders all over the world and all the socialists were joining resistance groups, dead or in camps.