No, you do not have to register a trademark in each member state of the European Union (EU). Instead, you can take advantage of the EU trademark system, which allows you to obtain trademark protection throughout the entire EU with a single registration.
The EU trademark, also known as the European Union Intellectual Property Office (EUIPO) trademark, provides protection in all 27 member states of the EU. By filing an application with the EUIPO, you can secure exclusive rights to your trademark across the EU.
This centralized system simplifies the process and reduces costs compared to registering individual trademarks in multiple member states. It offers uniform protection and avoids the need to deal with various national trademark offices.