The old “War Dept” Building is in Arlington and it is called the Pentagon. If you go to one of the entrances (Mall or River Entrance) their is a limestone cornerstone and plaque that states “Department of War”.
The Pentagon is WWII vintage, built to consolidate the War Dept in one place as it sprawled all over DC when the military ramped up.
When I moved to Arlington in the late ‘50s the area near the Mall was crowded with ugly “temporary buildings” still left over from WWII. I think Navy may have been using them.
The pre-WWII War Dept had been located in the OEOB and once shared space with State and the Navy. Prior to WWII our Army wasn’t all that big. Other than World War One our fights were mostly on North America, and after 1865 involved the Plains Indians.
The MARS (Military Auxiliary Radio System) once a year operates split band on HAM radio with civilian amateur radio operators on Armed Forces Day. I’ve talked to the Pentagon a couple times. Their call sign is Whiskey Alfa Romeo...WAR!