Greek Orthodox Church is a designator in English, not the name of an institution. Nothing answers to it as a single body, no synod governs under it, and nobody holds office in it. What it names is the family of Eastern Orthodox churches whose historic working language is Greek and whose rite, calendar and canon law took their settled form at Constantinople.
Four of them are the ancient patriarchates: Constantinople, Alexandria, Antioch and Jerusalem. Constantinople holds a primacy of honour among the Orthodox churches, which is the right to convene and to speak first rather than the right to govern. The bishop of Alexandria carries the title Pope and Patriarch of Alexandria and All Africa. Antioch and Jerusalem hold the ancient sees of Syria and of Palestine. To those are added the Church of Cyprus, whose independence the Council of Ephesus affirmed in 431, the Church of Greece, which declared autocephaly in 1833 and was recognised in 1850, and the diaspora archdioceses that depend on Constantinople in western Europe, the Americas and Australia.
What the designator does not cover is the rest of Orthodoxy. The Russian, Serbian, Romanian, Bulgarian and Georgian churches hold the same faith, the same councils and the same rite, and nobody calls them Greek Orthodox, because the word here records language and liturgical descent rather than communion. Reading the designator as the Church of Greece is the commonest error made with it, and it is an error of scale: the national church is one member of the family and not the family itself.