The Cypriot ccTLD registry has opened up direct registrations ie. company.cy
They appear to have changed the rules back in December of last year and are giving priority to registrants of existing 3rd level names eg. thing.com.cy
The wording on their site also suggests that the registrations are not in “real time” and that there is some form of manual review.
More details, though they’re quite scant, via the .cy registry site.
It looks like the .cy registry sells direct and does not have registrars. You’ll be prompted to register an account with them if you want to anything beyond seeing if a domain is available to register.