I wasnt able to find an explanation inside the GDPR whether a data privacy officer (or similar responsible) is allowed or required to document cases where individuals claimed the right to be forgotten.
Is it against the law to document the individual cases? edit for clarification: Such as "on Feb 26th Mr. John Doe inquired via e-Mail and requested to purge all his data". Now there is another data set about John Doe, documenting his deletion request, whereas he initially inquired to have his data erased. Instead of being forgotten, he is now remembered in one extra data collection. /edit
On one hand documenting the process allows a company to prove they obeyed the law and the request, should this be questioned later on by the individual.
I can even imagine a former employee first claiming his right to be forgotten, and then - a week after getting the confirmation - claiming his right to receive a resumee (a right in existense in Germany), which a company would not be able to fulfill as it hasnt got any data to base the resumee on. In case they do not have documentation, that the former employee requested to be forgotten, they cannot tell this.
On the other hand documenting such cases is 180 degree against the original request to be forgotten, as the individual ends up being stored in yet another data processing process.