This is actually not true! This is a pedantic point but I think is important.

The department of defense is not equivalent to the pre-1947 War Department. The War Department was in charge of just the army. There was a separate Department of the Navy. There was no over-arching department for all of the US military.

Post WW2 the US military was restructured to organize all of the branches (including the newly-formed Department of the Air Force) under a united civilian leadership. This was done in the National Security Act of 1947. The new structure was initially called the National Military Establishment and then renamed to the Department of Defense.

So the department of war name going away wasn’t a PR thing. It was because of military parochialism. If they had called this unified structure the Department of War it would have seemed like the Army was now taking over the other branches! And I promise you today’s Admirals understand that history, even if the secretary of defense doesn’t.