Why is Cyprus only country without a National anthem of her when few countries share the same eg Liechtenstein and UK?

This is not correct. Cyprus does have a national anthem, titled "Ύμνος εις την Ελευθερίαν" ("Hymn to Freedom"). It was adopted in 1966, following the country's independence from British colonial rule.

While it's true that some other countries also share the same national anthems, Cyprus's anthem is distinct and unique to its history and culture.