The president changed it back to its original name with an executive order. The administration did not just start spontaneously using it.
The president has no authority to do this. Federal departments and agencies are named by Congress, and even the Republicans in Congress have shown no interest in formalizing this.
No, the Department of War is the former name of the Department of the Army and nothing else. DoD is a new creation that includes the Army, historic Department of the Navy, and the other, post-WW2, new services.
"Changing it back" is completely ahistoric.