Very interesting to know. I have no clue when Germans began to call it that. It was called just „this war“ in the first years, and I don’t know when that changed.
In 1943, shortly after the Battle of Stalingrad, Hitler asked in an address, Wolt ihr den totalen Krieg? (do you want total war?) and his followers responded, chanting over and over again, Führer, befiehl! Wir Folgen! (Leader, command! We'll follow!)