Are you talking about whois data? NameSilo, Internet.bs and DynaDot are three registrars which offer free whois privacy that can be enabled before the domain is registered (purchased) or transferred. Your name might not be hidden from the registrar, but it will be hidden from the public.
ICANN rules mean you HAVE to give your name to at least the registrar when registering a name, so whois privacy is about the best you can do when it comes to people looking up the domain. If it's CC or other financial details you're worried about then go with a registrar that accepts Crypto and offers whois privacy, like NameSilo.