a corporate Anarchy wouldnt be an anarchy, its contradictory. because the Corporations would be governments. you could go farther and state that parents are governments over their children so, for their to be anarchy their cant be families. that is why when i state what i think the State should be like, i wont use the word, Anarchy.
i stopped calling myself Anarchist a long time ago, probably over a year, because it just confuses people, once you eliminate the current state, you can start calling things not normally considered government, government, such as businesses or parents. So i simply refer to myself as libertarian and say im for a "government" whose only job is to protect our liberties, to the point where our liberties conflict with other citizen's liberties; whether this is done by democratic election (unlikely), some type of monarchy, or oligarchy, or a company, or whatever, i really dont care.