Original: The name was borrowed from a different Austrian party active at the time (Deutsche Nationalsozialistische Arbeiterpartei, German National Socialist Workers' Party), although Hitler earlier suggested the party to be renamed the "Social Revolutionary Party"; it was Rudolf Jung who persuaded Hitler to follow the NSDAP naming.
Simplified: The name was borrowed from a different Austrian party active at the time (Deutsche Nationalsozialistische Arbeiterpartei).