> They changed the name

No, they didn't. The name of the department at issue is “the Department of Defense” and of its head the “Secretary of Defense” — these are set in statute (the latter for slightly longer time than the former) and the relevant statutes has not been changed, since the office of the Secretary of Defense was created in 1947 and the Department of Defense was created in 1949. The executive branch has just decided to use a nickname for a government department (which is the historical name for a prior department which was split to form two of what are now the three main direct subordinate elements within that department.)