...was "socialist" in name only. Surely you're aware of that?

In actual practice, the NSDAP was in bed with Germany's powerful industrialist concerns and even "reprivatized" some previously nationalized businesses. They abolished labor unions, replacing them with a single umbrella organization (the DAF) that performed zero worker advocacy and concentrated solely on increasing production efficiency. The closest the NSDAP came to real socialism was a high degree of regulation of the economy, but this was not much greater than that seen under wartime footing among the Allied powers.

The use of the term "socialist" by the party was basically as a marketing tool, designed to appeal to a struggling working class and to differentiate themselves from both the communists and the traditional factions in post-WW1 German society.