W.S. Allen wrote an excellent book on this subject, 'Vox Graeca'. I am of the opinion that ancient Greek must have sounded considerably different to modern Greek (consider for a moment just how much Greek grammar has changed), and Allen's arguments are generally conclusive. Certainly in my Greek philology lectures we would transliterate the word as 'Demetrios'. The 'eta' was roughly pronounced as an elongated 'eh' sound, not as an 'i' sound as many Greeks often state (I don't wish to generalise, but all the Greeks with whom I have spoken on this subject are remarkably naive, imagining that their form of the language is exactly the same as the Classical form).