Suppose that I want to form a company in the US while keeping my information and that of my co-founders private. How could I go about doing it?
Get a corporate lawyer. The standard practice is to create two LLCs (usually in Delaware, which offers some of the best protections): A holding company owned by the individuals, and an operating company, owned by the holding company. If done correctly (which is why you need a lawyer to review the creation and operating agreements) it is nearly impossible for an adversary to follow the operating company back to the individuals without a compelling legal reason ordered by a court.