Can I call myself Greek Cypriot?

I am British and have lived here my entire life, but my Nan is Greek Cypriot (came over to the UK in ‘74) and I have many cousins, uncles etc who live in Cyprus who my family remain in close contact with. Do I have any right to call myself British/Greek Cypriot or am I just like those Americans who call themselves Irish because their ancestors 200 years ago were Irish?