The term "personally identifying information" does not occur anywhere in the text of GDPR; the regulations use the term "personal data", which is defined differently.
I raise this issue in almost every thread about GDPR, because although it might seem pedantic, the error strongly implies that people have not read or understood the legislation. The difference between personal data and personal identifiers is integral to GDPR and the legislation cannot be understood without fully understanding that distinction and the implications that follow from it.