Why would you want to register a website and make it private if you goal is to sell it? Is there a way to register a site and only have your email address the contact information?
You make your domain information private so nobody can see who owns the site or can call you, most do it cause illegal content or most do it because they want to. Whatever you want to show on your website you can put but the domain contact information is up to your domain register on the information you signed up as. Now, on the domain if you put your real info, you can purchase privacy and have your name, address, phone , everything off so whenever somebody looks on a website like who-is.net they will just see the domain company's info, not yours, but if you want yours don't purchase the domain privacy and all your info will show you used to sign up the domain account under.