Byzantium is also more properly the name of a town, which was refounded by Constantine as Nova Roma or Constantinopolis. I'm not sure how or if this should be worked in.
Don't each name concern a different time period? There's a lot of history to be covered for this town, eventually, so I think it'll probably help organization to have it split (even if it means that a few sentences will be duplicated). --Pinkunicorn