No. In contrast with the EU Data Protection Directive of 1995, the GDPR does not require you to register your databases with the Data Protection Authority (DPA). However if you appoint a data protection officer in your company, you should send the DPA his or her contact details.
Under the GDPR, you need to appoint a data protection officer if:
you are a public body (e.g. ministry, school, public hospital);
your business involves regular and systemic monitoring of people’s data on a large scale (e.g. big tech companies, or companies that do credit scoring or video surveillance); or
you processes sensitive data on a large scale (e.g. hospitals).