I had always heard it as "Yeddo", but then the other night the Japanese actors in the new Shōgun series seem to favor the un-glided "Edo," and looking it up on jisho.org I find that the furigana give it as えど, though they quote Wikipedia in saying that "Yeddo" was used for purposes of romanization.
It seems to me that if we believe the furigana, there is no "y-glide" to start the first syllable. Why would we need to add one for romanization? It is exceptionally clear to me that English, at least, has no trouble pronouncing the initial /e/ in egg or Ed or Eminem, so why should the glide be necessary?
Is there no single pronunciation of the city in Japanese? Or has the one with the glide changed over the centuries into the one without?