I never looked into it until today, and apparently the names aren't as different as I thought:

“We are not sure how [the name Istanbul] was developed as it emerged from the Greek and we are not sure how far it goes back,” Ahmed says. “It means to the city, so if you see the word Constantinople it has the word Stan and Pol in it as it was called Constantinopolis. It simply means I Sten Pol meaning within the city, probably meaning within the old city walls.”

Why did Constantinople get the works? The name was too long for the Tuuuurks!