They called themselves the "Deutsches Reich" (1933–43) and then the "Großdeutsches Reich" (1943–45). The term "Third Reich" comes from the belief that they were the successor state to the Holy Roman Empire (First Reich) and the German Empire/Deutsches Kaiserreich (Second Reich).

Source:

van Wie, Paul D. (1999). Image, History and Politics: The Coinage of Modern Europe. Lanham, Md: University Press of America.

Lauryssens, Stan (1999). The Man Who Invented the Third Reich: The Life and Times of Arthur Moeller van den Bruck. Stroud: Sutton.