I too thought Istanbul was from the eis... phrase, but the Constantinople origin is fine by me. The change exhibits a number of features common to Modern Greek: loss of initial syllable (e.g. vrisko from ancient heurisko:), voicing of voiceless stops after a nasal, and (in the older form Stamboul) assimilation of the nasal. In Modern Greek ton polis is pronounced tom bolis.

The initial I (with a dot on it) is Turkish, which does not tolerate some initial clusters, and uses the i to make them pronounceable: so 'sterling' is isterlin.

Afterthought.

If Persian ostan (which by the way is the name of some of the internal divisions of Iran) is from the IE root 'stand' then it's probably related to state, from the Latin, and to the English stead 'place' as in homestead, bedstead, Hampstead, instead, and steadfast.

In German, Staat 'state' is presumably from Latin while Stadt 'city' is the native Germanic reflex, corresponding to English stead and Icelandic -stadhur.