Basically, there is no need to send data to the authority. Not even your record of processing activities (ROPA) is automatically being transferred to the authority.
The regulating authority only demands that you document the processings of personal data and that you can provide that documentation for the authority on demand. The authority doesn’t find out any specific data (e.g. names or email addresses) thereby.
Only in certain cases the authority is going to ask for specific data, e.g. if somebody files a complaint, the authority is going to ask for data of that person so that the authority can verify the complaint.