To my mind, calling them Greek is a bit like calling people in, say, Belize "English". If I brought a vase from Belize and said "I brought you an English vase", would you not find that odd?
Just because someone speaks a related language (and I'm pretty sure the Greek of Constantinople was different from the Greek of Athens at the time), doesn't mean that they are the same people. The Byzantines had hundreds of years as a distinct culture from the Greek islands and peninsula, with a major Roman influence.
Just because someone speaks a related language (and I'm pretty sure the Greek of Constantinople was different from the Greek of Athens at the time), doesn't mean that they are the same people. The Byzantines had hundreds of years as a distinct culture from the Greek islands and peninsula, with a major Roman influence.