It is, perhaps, easy to forget that 'Nazi' is not the proper name of the infamous political party and movement, but a contraction of the name. In full it was the National-Socialist German Workers' Party; in German, this name is 'Nationalsozialistische Deutsche Arbeiterpartei', represented by the letters NSDAP.

The Party started life as the German Workers' Party (founded January 1919) and was then renamed by Hitler as the NSDAP in the early 1920s. In the German language, it was -- and is still -- quite common to form familiar contractions from lengthy official titles. Thus the 'Geheime Staatspolizei' (Secret State Police) became known everywhere by the terrifying name 'Gestapo' (Ge+Sta+Po). The term 'Nazi' came from the 'Na' in 'National' and the 'zi' in 'sozialistische'.

The picture is of the NSDAP Administration Building, München (Munich).

More Info: en.wikipedia.org