The oath that military officers and civil servants take does not mention the President at all:

"I, [name], do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I take this obligation freely, without any mental reservation or purpose of evasion; and that I will well and faithfully discharge the duties of the office on which I am about to enter. So help me God."

Source: https://en.wikipedia.org/wiki/United_States_Uniformed_Servic...