If I understand this correctly, someone can register for a private domain name, then transfer it to a hosting site. After this is done, your domain name will still be privately registered. Is this correct? I ask because I want to host my site with a certain web hosting company, but they do not do private domain name registration.
As long as you know the ip address of the name servers that you should be pointing at then you can make your own custom domain name servers. You can do this using Godaddy, I dont know about others.
This is not what KrazyKat has asked. Private domain name registration refers to privacy protection in whois. KrazyKat, are you transferring website as well as domain to your new hosting provider?