The name is verified by in-game jukebox.
Wolfenstein 3D (DOS)
This song is played in E2M1, E2M5, E5M1, and E5M5.
Nazi Anthem is track number 9 in the data files. Its title in the IMF meta data is "NAZI-OMI", which might mean "Nazi Omnibus" or "Nazi, Oh My!". This song is not included in the shareware version of Wolfenstein 3D.
This song was composed with Sequencer Plus Gold.
Spear of Destiny (DOS)
This song plays at the level 11.
It also have number 9 and title "NAZI-OMI". It's not included in the demo version of Spear of Destiny.
Wolfenstein 3D (GBA)
Wolfenstein 3D (WEB)
Wolfenstein 3D (GEN)
In Genesis port, Nazi Anthem is only presented in sound test menu. Probably it's because GASEGA68K, game's porter, couldn't create second episode, but was ready to do this, so he arranged the rest of the music just for future.