It grinds my gears how people call those Gyro-eating, Ouzo-drinking, Greeks as "Eastern Roman Empire". Bah, they are as much Romans as the "Sultanate of Rûm". Just because the Empire was partitioned waaaaaaaay back during Augustus rule, it doesn't mean that they were Romans way that late! From the moment Western Rome fell, Eastern Rome lost its privileges to be called Rome! There is nothing Roman about them, not their tongues, not their clothes, not their culture, their poltiics, or even their military tactics!
Remember the rule, in general, when historians convene and decide that they should be called BYZANTINES, it is probably better to agree on it, they know their trade.
And before anyone comes with the "hurr durr they were officially called Roman Empire", let me tell you that the Austrian Emperor was officially King of Jerusalem, yet I don't see a bunch of internet dwellers thinking themselves fancy to call the Austrian Emperor "King of Jerusalem". A claim is a claim, and what the Greeks had, was nothing but a claim.