It might depend on the domain. For both .com and .net domains everything I've registered has only listed "Moniker Privacy Services" as the domain owner. I have a friend that registered a .org.uk domain and it listed his name, but address/phone/etc were hidden.
Enterprise Network Engineer :: Hosting Hobbyist :: Master of Procrastination
"The really cool thing about facts is they remain true regardless of who states them."
Moniker Privacy Services registers acts as the Registrant of record for any domains you choose WhoIs Privacy for. Even though Moniker Privacy Services is listed as the Registrant, you still control the domain and retain the full benefits, responsibilities, and ownership of the domain name registration.