You have two options.

Use a corporation name but that will still allow someone to view the officers of the corporation in most if not any state.

Or use the option to keep the registrar information private, which I believe is extra.

I would create a corporation, use that to register the domain and then use the option to keep the registrar private.

if you use your real name buy  privacy protection so no one can see your real name on whois.

Please, i ask that you DO NOT support Go Daddy, unless you really hate elephants.

Bob Parsons, the CEO of web hosting company GoDaddy.com, recently posted horrific footage of himself hunting and killing an elephant during a vacation to Zimbabwe. Worse, he seems to think himself a hero and defender of the Zimbabwean people he is visiting. But Parson's high powered rifle and ill-considered vacation aren't the solution to anyone's problems.

Elephants are intelligent, incredibly social animals, and their packs have been devastated by poaching and people like Bob Parsons hunting them for perverse entertainment.

eNom will allow private registration. When I registered my domain, I used their privacy feature and then did a whois search and my private info is not in there.