This sounds ultra fishy, but it really is just for keeping a certain person from determining who is behind a company. I want to start a business with a business name, in any state, and not have my name publicly available.
Obviously, the state and federal governments would have to be able to track it down so that they made sure I paid taxes, and that's fine. I just don't want anyone to be able to go to a courthouse or government building and have public access to see that it's me who owns it.
I believe the closest you'll get is incorporating in Nevada. That protects the names of any stock holders in the company, though you may need to work with a company specializing in this to get your name completely off of the books.
Edit: Actually, since you have to disclose the name of the business owner in Nevada, Delaware appears to be your best option since that has privacy for the owner names from the public. Nevada has complete privacy of share holders even from the IRS, which you mention you don't need (and really, why should anyone).
Provided your name does not appear in incorporation documents, you will not be identifyable but that means you do not have an officer or director position. If this is an attempt to shield assets, there are other ways to do that.