You've got that backwards. Originally stemming from the War Department, the "Department of Defense" is a cuddly name so Americans can feel better about, and potentially ignore, being warmongers.
No, I don't. The legal name of the Department headed by Pete Hegseth is the Department of Defense, and it is the only name that entity has ever had.
> Originally stemming from the War Department
This a somewhat popular myth, resurgent recently because it is expressly part of the narrative of the Trump Administration and therefore the MAGA cult, but its false. The Department of War is the predecessor of the modern Departments of the Army and Air Force which it was split into, not the Department of Defense, which was created ex nihilo to be placed over the existing military departments at the same time one of those department s was being split.
Originally, the US (following the British model, which also persisted until just after WWII) had two separate defense edtablishments, the Department of War (responsible for the Army) and Department of the Navy (responsible for the Navy and Marine Corps); after WWII a combined defense establishment was created above those, but at the same time it was created, the Air Force was split off from the Army and the War Department was split into the Department of the Army and the Department of the Air Force, which is why the Department of Defense is the only cabinet level department with subordinate entities also called “departments”.
I am saying that it is not the legal name of the Department. As far as I know its not illegal to refer to it as the Department of War, the Fighty Bunch, or Bob, but it is weirdly unprofessional to just start calling givernment departments by random made up names that aren’t what they are specified as in law.