You are pretty much describing the premise behind Max Berry’s book - Jennifer Government.

In the alternate present the novel portrays, the United States has taken over all of North and South America (except for Cuba) and dominates much of the rest of the world. The United States adopts “capitalizm”, a form of minarchy that abolishes taxation and privatizes government.

People take the names of the corporations that employ them as their surnames, and persons with two jobs hyphenate their name, e.g. “Julia Nike-McDonald’s”. Employees of the government, including the novel’s title character, take the surname Government.