Is there such a thing as Cypriotism?

It’s a very little used word, but yes:

Cypriot nationalism – Wikipedia

Cypriot nationalism, also known as Cypriotism, refers to one of the nationalisms of Cyprus, a shared identity of Greek Cypriots and Turkish Cypriots highlighting shared economic, political and social rights. Cypriot nationalism supports the reunification of Cyprus under a federation and the end of foreign interference (by Greece, Turkey and the United Kingdom).

If you’re asking whether Cypriot Nationalism has any potency as a force driving the reunification of Cyprus: my impression is, non-zero, but not much. But I don’t live there.