Kiev regional domains .kiev.ua /.kyiv.ua are mirror to each other. This means that if you register one example.kiev.ua domain, the second example.kyiv.ua domain is immediately reserved for you as a mirror. No one except you can register it, since mirrored domains can have only one owner.
It is possible to register a mirror domain only with the same registrar where the first domain is served.
If you already use one of the regional Kiev domains, to register the second (mirror) domain, please contact NIC.UA support.
If you already use one of the domains with another registrar, but wish NIC.UA to assist your second domain, transfer the existing domain to NIC.UA first, and then contact us to register the second mirror domain.