If I register a .GR domain name is there a possibility that the same domain could be registered by someone else with the same .GR TLD?

Reply: 

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