A name doesn't say much. In post-war Germany, one post-Nazi party founded by ex-Nazi member Franz Schonhuber was called the Republicans. The current neo-Nazi party is called the National Democrats. Parties are usually given names with words that are popular at the time and don't have much to do with ideology.

The Nazis did have a socialist wing at the beginning, the Strasserites. However, this wing was purged. One of the Strasser brothers escaped into exile in Czechoslovakia, while the other one was killed in the Night of the Long Knives Purge in 1934. After this purge, the Nazi Party for the most part had a right-wing ideology and worked hand in hand with the big German industrialists.