The information used to register a domain name (be it a .EUS one or any other) is public and anyone may consult it. We at the PuntuEUS Foundation have developed a tool designed to facilitate that consultation: whois.eus.
You can use whois.eus to look up information about any domain name. All you have to do is write the domain name in the search box and run the search. Various items of information about the domain name consulted will be displayed; they include who registered it, when it is due to expire, or which registrars are managing it.
The domain name consulted may not have been registered. In that case, the search box will inform you that no results have been found.