[dghf]

> For those who don't know it, this is the name the department has had for most of its history

Not really. It's the old name of the Department of the Army. Except for the first nine years of the DoW's existence, the Navy had its own, independent department, as did the USAF once it was established as a separate branch.

The Department of Defense didn't exist until after WW2, and was called the National Military Establishment for the first couple of years.

You see a similar pattern in the UK, which had the War Office for the Army, the Admiralty for the Royal Navy and the Air Ministry for the RAF: after WW2, the Ministry of Defence was created, initially liaising and co-ordinating between the service ministries, and then fully absorbing and replacing them.

tl;dr the Department of War is the old name of the Department of the Army, not of the Department of Defense.