How did the department of war change in terms of its name and organization?

The Department of War became the Department of the Army which was then folded, along with corresponding departments for the other branches, into the Department of Defense.

It used to be that each branch was its own department, with its own cabinet-level secretary. After World War II, the entire security apparatus of the United States was reformed and Congress created an overarching department, the Department of Defense, to run the entire military in an effort to reduce political infighting and operational confusion. Each branch's individual department and secretary all reported to the Secretary of Defense who took over their spots in the Cabinet.
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