Keep in mind that you cannot register a .eu domain name through EURid.
You can only register a .eu domain name through an accredited .eu registrar.

That's because registering a domain name through a registrar is a little like buying books from a bookseller. A registrar usually provides services for many different Internet domains, including .eu, just as a bookseller sells books from many different publishers.

Check the .eu WHOIS database to see if the name you want is available.
Read the WHOIS policy for more information.

Any accredited .eu registrar can help you register your .eu domain name. If you don’t have a registrar, you can find one by searching our registrar list.

A special logo appears next to the registrars who have signed
the .eu Code of Conduct agreement.

Registration fees are set independently by individual registrars.