We are speaking of the church calendar. All Christian churches (there was no single "Eastern" church) as far as I know used the Julian calendar (named after and instituted during the reign of Julius Caesar) until Catholic church adopted Gregorian calendar.

| All Christian churches (there was no single "Eastern" church) as far as I know

There is the Eastern Orthodox Church (Russian Orthodox, Greek Orthodox, Bulgarian Orthodox, Georgian Orthodox, Ukrainian Orthodox, etc.) - This is all one Eastern church.

There is the Oriental Orthodox Church (Coptic Orthodox, Syriac Orthodox, Ethiopian Tewahedo Orthodox, Malankara Orthodox, etc.). This is all another Eastern Church.

There is also the Assyrian Church of the East, but ever since the war in Iraq and rise of ISIS, it's all but destroyed at this point.

Between those 3, those are the only "eastern" churches in existence apart from tiny schismatic groups. However, when someone refers to the Eastern Church, they are almost always referring to the first one, the Eastern Orthodox Church, since it's enormous and sat at the center of the Byzantine Empire.

I think there's a confusion between classification and hierarchy. I would always use the plural when referring to Eastern and even more so Oriental Orthodox Churches. They are independent entities, though they have affinities to each other and can be grouped together based on what ecumenical councils they recognize.

In contrast, there is single Catholic Church, and just a century prior to Gregory's time it united all Christians in the Western Europe, apart from a few heretical / protestant movements here and there.

They don't view themselves as separate, they view themselves as part of a unified whole. It seems very strange to pluralize them when they don't even pluralize themselves.