The owner of the domain (but the correct name is the domain holder, as this person does not own the domain) can be found in the central domain registry. This is different for each ending.
Holders of Czech domains can be found in the central registry of Czech domains, called CZNIC, which is available at nic.cz. Enter the domain you are looking for in the search box and you will see who the domain holder is in the search result. You can still click on it and see more detailed information. Some of this information may be non-public and cannot be found out.
Holders of Slovak domains can be traced at the Slovak central registry SK-NIC via the search box. After the search, detailed data can be displayed.
They are called generic because they are not national. Finding out who owns them is a bit more complicated. For example, a domain can be looked up at Joker.com, which is one of the generic domain registrars that offers this option. Try searching for the domain test.com for example, you will get this result:
Where it says Registrant you will find the details of the domain holder.