lots of people pay for privacy service for whois info
paying extra to use a privacy service for the whois is pretty common, and a good idea if you personally register a domain. you don't want your home address and real name attached, right?
And so nothing really changed except that, with GDPR, it's theoretically possible to get the same level of service FOR FREE.
Let's do that in the USA too! I like it already.
In theory a registrar would need to have the real name/address and so they would know who to serve paperwork on for any kind of legal action.
That being said, ICANN could require registrars to cooperate with 'due process'. Fixed.
[it's probably like this already for the privacy services]
In the USA, you could do something _like_ an 'order to locate' in which you submit paperwork to a judge, in an 'ex parte' hearing (meaning you walk on in between cases) who then reviews the request and then signs or rejects it, most likely signing it if the case it applies to has any kind of merit. Then you serve paperwork after locating the entity/individual, sometimes involving law enforcement in the service, etc..
The registrar would simply have to honor the judge's order. But it's an extra step, probably doesn't really cost anything more than attorney fees for paperwork, and that will be significant enough for any legal action, so it's like *meh*.
IANAL disclaimer, YMMV, etc.