President Donald Trumps speaks alongside Secretary of Defense Pete Hegseth, second from right, and Gen. Dan Caine, chairman of the Joint Chiefs of Staff, during an event in the Oval Office in Washington, on Friday, Sept. 5, 2025. Trump’s executive order authorizes the Department of Defense and the secretary of defense to be called the Department of War and the secretary of war. It is unclear how it will be formalized given that Congress approved the name. (HAIYUN JIANG/The New York Times)