Anonymity to the general public is very easy, incorporate a company behind some of the shell corporation mumbo jumbo that any corporate lawyer can prep for you, it will cost $ but it will be easy.
Anonymity from Apple could probably be pulled off by incorporating in a country with fairly weak transparency and having the company owned by an offshore trust.
Anonymity from a state level actor would be pretty hard. You'd have to have a shell corp in a foreign country owned by a shell corp in another foreign country and even that might not be enough.