The answer is No. Papaki is in charge of all .GR domain name registrations. This means that once a .GR domain name is registered, it cannot be registered by someone else as well. However, have in mind that someone might have the same name with a different tld. For example, you are the only owner of the domain name.gr, however someone else may also own the domains name.com, name.eu , name.de and etc. All .GR domains are registered at the National Board of Telecommunications and Posting.