How did Istanbul get its name?

Istanbul probably means nothing more than "the city." It is a Greek phrase that Turkish speakers took for a name.

The older name was Constantinople, from the Greek Konstantinou polis, "Constantine's city." Etymonline says it honored the Roman emperor Constantine, who moved the Roman capital there. The name was used from 330 to 1930. Before that the city was Byzantium, founded by Greek colonists from Megara around 667 BC, according to Wikipedia.

The word Istanbul comes from how people spoke about it. Etymonline traces it to the Greek phrase eis tan (ten) polin, glossed "in (or to) the city," which local Greek speakers used. Wikipedia gives a close variant, medieval Greek stin Poli(n), "in the city." A 2015 review concluded that the meaning was probably "in Constantinople."

Turkish does not allow a word to start with "st-", so an i- was added at the front. The result was Istanbul. Wikipedia says forms without the initial i- appear in 10th-century Arabic sources, and in Armenian sources by the 12th century. It adds that the Arab historian al-Masudi wrote that the Greeks called the city Stanbulin.

A second explanation is folk etymology. Turks have traditionally linked the name to Islam bol, roughly "plenty of Islam." Wikipedia reports that the form Islambol did appear after the Ottoman conquest of 1453, and it was used on coins in 1730. But Etymonline treats it as a folk explanation, not the source.

The Ottomans used both names. Wikipedia says Istanbul was the common name in speech, though that point is flagged there as needing a citation. Kostantiniyye was preferred in some official contexts. Istanbul originally named only the core walled city.

The change to a single name was political. Wikipedia says Turkey asked other countries to use Turkish names from 1930, and the US State Department adopted "Istanbul" that May.

So Constantinople gave way slowly. The everyday name, a Greek phrase for "the city," took over.