The bumper sticker you see on many cars "coexist", spelled out with the symbols of different religions, forgets that the first letter stands for islam, and islam never coexists. It only waits for the chance to destroy and conquer.
Was the area covered by most of the Orthodox Church conquered at one time by Islam. Did they submit and stop referring to G_d as Yahweh? Did the term “allah” come in, when those areas were conquered?
Unfortunately muslims object to Christians referring to the G_d of the Bible as allah. Christians have been arrested and tried for doing so in other muslim countries.
Pretty much yes, with the exception of Orthodoxy in Russia and the more northern parts of Eastern Europe.
"Did they submit and stop referring to G_d as Yahweh?"
I suspect that we never called God Yahweh. In the Balkans God was called, as I said, Ο Θεος or more formally as in icons, Ο ΩΝ. Greek was the common language back then. There were (and are) Christian people in what is now Syria, Lebanon and Jordan/Israel who spoke Aramaic (ʼĔlāhā, or Alaha) and others who long before the Mohammedan conquest spoke Arabic. Submitting to the Mohammedans politically came later.
"Did the term “allah” come in, when those areas were conquered?"
No, it came in before. As you can see, the Aramaic/Assyrian word is almost identical to Allah. Aramaic is the language Christ used.