"I am pleased to announce that the Great Elon Musk, working in conjunction with American Patriot Vivek Ramaswamy, will lead the Department of Government Efficiency (“DOGE”)." - President-elect Donald Trump in a statement
It does not appear that a US president can unilaterally create a new government department. This requires congressional authorization to allocate funding and the establishment of the legal framework for the department's responsibilities, scope and oversight.