Anatolia was once a Christian nation which spoke many languages, including Koine Greek. Then around 1000 AD, Turkic tribes calling themselves Seljuk came from the East, and about 500 years later, they conquered Constantinople and renamed it as Istanbul. At this point, they became known as Ottoman after Othman.
But why the change? Is it because the original Seljuks were so different culturally, ethnically, etc. from their later selves?
It might be more accurate to talk about a change in dynasties, but that is also inexact. Also the timelines you propose are wrong, the Ottomans had been stablished for over a hundred years (ca1300 depending on what you consider its beginings) by the fall of Constantinople in 1453. During the Seljuk wars against the Byzantines Constantinople was taken and looted by the latins of the fourth Crusade, but never by the Seljuks themselves.
The change came after 1243, with the Mongol invasion. The Seljucid empire was already weakened by internal fighting and was further fractured by this event. As this happened the empire lost control over several warrior tribes settled in the frontier to Byzantium, several of which became principalties. One of these was what would become the ottomans, though etnically they were the same: oğuz turks originaly from the china/mongolia border, muslims before they even left that area. The last part of the Seljuk Empire, the Sultanate of Rum, was conquered by the Karamanids in 1328.
What would become the ottomans started as a principalty by Ertuğrul, but it is his son Osman (turkish Othman) who gives the name by which they will be known. He inherited the principalty around 1285 and started to gain territory by raiding the Byzantine countryside, capturing their first mayor city, Bursa, in 1326. Following this they quickly gain more power and territory, first to the west and more gradually eastward, first by gaining the alegiance of other tribes and later through conquest.
This is a rather quick and dirty summary, but i hope i answered your question.
I don't have the answers your questions. I'd note, however, that the name Constantinople continued to be the official name of the city. It was following the formation of the Republic of Turkey, in 1923, that the city's name was officially changed to Istanbul. This is an Ottoman coin featuring the name Constantinople, struck in ~1909.
