I would say where you process the data really matters, but not for applicability of the legislation.
Processing GDPR Personal Data with no third country adequacy, no BCRs, model contracts etc - and the controller and processor are going down.
A quibble, but one I think that reinforces your point.
As the Economist states :The world's most valuable resource is no longer oil, it is data".
This is my understanding : the First name and Last name combine to create a single entity = Name - because name is not in itself a unique identifier it requires another primary element to constitute PII. there are instances where the actual name is unusual in its construct ( spelling, pronunciation etc.) but a secondary element is still required to make it identifiable - Happy for anyone to comment and disagree