Having looked up the etymology of Istanbul I was surprised to find "Constantinople" just wasn't relevant to how Istanbul came about, with Istanbul being a Turkish corruption of Stamboul from eis tḕn Pólin with it's own origin and everything.
Was that it? The two city names sound similar and it's just a coincidence they do?
For all I know, eis ten polin is just a pun in a way. Sounding close to Constantinople and referring to Constantinople, but being a different phrase itself. Just like how nobody would normally say something like "Sauce?" when asking for a source if not for the fact the two words sound similar. Do we have an answer for this? Is it just a coincidence like it really sounds? Are the two linked in any way?
It isn't entirely a coincidence. The etymologies:
Constantinople: From Greek Κωνσταντινούπολις, (Kōnstantinoupolis), "City of Constantine" or "Constantine's City"
Istanbul: From Greek εἰς τὴν Πόλιν (eis tḕn pólin), "to the city"
Both "ple" and "bul" come from the same Greek word (πόλις, polis, "city"), and the similarity of the endings of the two names for the city is etymological, not coincidental.
The similarity of the first part of the names (which are IMO much less similar) is coincidental.