Okay, here goes.
Istanbul was originally known as Byzantium. Emperor Constantine rebuilt the city as his capital and renamed it Constantinople; literally, City of Constantine. When the Roman Empire split in two, Constantinople remained the capital of the Eastern Empire. When the Western Empire fell, the Eastern Empire became known as the Byzantine Empire or Byzantium, for somewhat obvious reasons. Eventually, the Ottomans conquered Constantinople, possibly the greatest city in Europe at the time, and made it their capital.
The Ottoman Turks did not change the city's name. It remained their capital, retaining the name Constantinople, until after Mustapha Kemal (later known as Kemal Ataturk) successfully led the Young Turk Revolution against the last Ottoman Sultan, and made Greece and Armenia his biatches. He moved the capital of the new state of Turkey to the more centrally located Ankara - which, incidentally, used to be known as Angora. The language has changed over the centuries - and eventually, years later, changed the name of Constantinople to Istanbul. This had nothing to do with Christianity, it was just another of Ataturk's many moves to break with the past.