Gyros, which is pronounced jai-rose in Australia, I have been led to believe, is actually pronounced Ghee-ross in Athens, where I encountered it as a cheap meal whilst travelling overland from London to Istanbul. The Greek word is γύρος (gyros, 'circle' or 'turn'), and is a calque of the Turkish word döner, from dönmek, also meaning "turn". It is the meat that is cooked as it turns on a large upright skewer against a vertical grill. The way it was served when I had it was thinly-sliced on a small freshly made unleavened bread, like a pita only thicker, with tomatoes, onions and a paprika-like spice sprinkled on top.
Roman Empire should be accepted for Byzantine Empire, or at least Eastern Roman Empire. Especially if you choose to have a map of the empire under Justinian, a native latin speaker.
But well I wont go as far as saying that therefore it cant be apollo. The gods were quit known to shapeshift. Dont know about apollo specifically