The name is relatively meaningless in terms of the bigger picture of German history despite the importance some corners of reddit place on the S. For one thing, the NSDAP's original name was Deutsche Arbeiterpartei (German Workers Party/DAP) and it changed to the more familiar NSDAP in 1920. To show how little this meant, the Party archives never really recorded why they made the change in the first place. There are a number of interpretations as for this renaming. One view was that the Munich Party was trying to form closer bonds with Austrian and Czechoslovakian right-wing groups, also called national socialists or some other variation on NS. Another theory, and one that fits within the Party's larger history in this period was it was part of Hitler's attempt to make the Party more dramatic. This was less about incorporating socialism into the Party's program and much more about trying to widen the visible profile of the Party in the contentious Bavarian politics of the 1920s. Renaming could have been part of the larger repackaging of a really minor political party by Hitler to be make a bigger impression. This campaign included such symbols as the swastika banner and greater prominence given to the SA in Party rallies. The clumsy NSDAP acronym was partly an attempt to cast as broad an ideological net as possible to draw in new recruits, but there was an element of provocation about it. NSDAP posters in this period often dared the German left to attend Party gatherings using familiar symbology that had been the preserve of the left such as the color red. Hitler was quite open both in Mein Kampf and his own interviews that this was trying to court violence and cause a stir. As he would claim in the 1920s:

It makes no difference whatever whether they laugh at us or revile us, whether they represent us as clowns or criminals; the main thing is that they mention us, that they concern themselves with us again and again.

So the S meant about as much as the N,D,A, and P in the early 1920s. If it drew in a few new members from the left, then so be it, but the NSDAP rebranding was not part of a larger program to incorporate socialism into German far-right politics.

Similarly, the Nazis never disavowed the S once in power, but Nazi discourse invariably used Sozialismus/sozialistische in combination with National or, more uncommonly, German. This conceptualization of socialism was deeply intertwined with racialist thought to the point where Nazi ideologues claimed socioeconomic distinctions were irrelevant given the natural instincts of racial solidarity. The dictatorship put incredibly little effort or interest in redistribution of Aryan wealth or restructuring the German tax codes. Whether through the voluntary one pot Sundays or donations to the Winter Relief, the socioeconomic leveling under National Socialism was to be voluntary. State levers of coercion to get Germans to volunteer were present but not monipresent. Not surprisingly, while many Germans participated in these programs there was a widespread sense that not everyone was pulling their fair share. The Third Reich's schema that divided the German people into a healthy Volkgemeinschaft composed of all walks of life and various racial traitors encouraged the social formation of in- and out- groups.

The state's intervention in the economy may have been severe, but it was not really to alter the socioeconomic fabric of Germany. Nationalization or quasi-nationalization through the command economy was related to rearmament far more than any restructuring of the economy and its people. The state might use the stick to bring industry to task for rearmament as it did with the Junkers firm, but both it and industry was much more comfortable with the carrots of a German-dominated European economy, state siding with industry over labor, and the promise of expropriated property of non-German and Jewish rivals. The state may have capped profits, but Germany's corporations often used the state to maximize capital investments and prepare for an immediate future where Germany and its private enterprises would dominate the continent. By the same token, the state seldom intervened to shut down small-scale or medium -sized private enterprises, even if doing so could lead to greater rationalization of the economy or better use of scarce German labor. The proprietors of these establishments were often the middle-class burgerlich bedrock for the NSDAP's support.

With this in mind, portraying the Nazis as left-wing because of its S is just absurd.