I read the link provided. Clearly Dynadot doesn't hide the fact that the definition of private registration is different at Dynadot than it is for what most people know is the correct definition, imo.
It is misleading no matter how much explanation is given, for dynadot to offer a private registration that dynadot knows is not fully private.
ICANN recognizes that the owner of your domain is the person listed as the Registrant. This can present several problems that we want to avoid.
ICANN set the rules for how WHOIS information must be displayed. We have to work within that system, if Dynadot's name was entered as the Registrant, we'd be the owner of the domain.
I think that is rather bad. I think privacy should pay for the right to not have your name shown. Why is it not reasonable that just the registers name be shown?
You currently only have privacy applied to one of your domain names.
Our privacy service only replaces your contact information. Your name remains on the WHOIS record in order to prevent confusion about who is the owner of your domain name.