Short answers, pulled from the story.
The oldest recorded name for Istanbul is Lygos, preserved in Pliny the Elder's Natural History. Its origin and meaning are unknown. It may have referred to a Thracian settlement near the tip of the peninsula now known as Sarayburnu.
Istanbul derives from the colloquial Middle Greek phrase 'στην Πόλι(ν),' meaning 'in Constantinople' or 'to Constantinople,' according to a 2015 review of the scholarship. The Greek word for city, Polis, sits at the root of the name. The initial i- was inserted later to break up a consonant cluster prohibited in Turkish phonotactics.
Turkey formally requested that foreign countries adopt Istanbul in 1930, following an alphabet reform in 1928. The U.S. State Department switched to Istanbul in May 1930. Most modern Western languages adopted a form of the name during the 20th century.
The Ottoman Empire used Kostantiniyye as its most formal official name for the city after the 1453 conquest, keeping it in use until the empire's fall in 1922. A third name, Islambol, appeared after the conquest and reached official use between the late 17th and late 18th centuries, first appearing on coinage in 1730 during the reign of Sultan Mahmud I. The Ottoman constitution of 1876 declared the capital's name to be İstanbul.
Byzantium was the name given by Greek colonists from Megara who founded a settlement on the site in 667 BC. The name is believed to be Thracian or Illyrian in origin, predating the Greek arrival, and may derive from a personal name, Byzas. Ancient legend identified Byzas as the mythological king who led the colonists and gave the city its name.
Medieval Vikings, known in Byzantine sources as Varangians, called the city Mikligarðr, combining the Old Norse words mikill, meaning 'big,' and garðr, meaning 'wall' or 'stronghold.' The name appears in the Icelandic sagas, which record the Vikings' contacts with the Byzantine Empire through their expansion across eastern Europe.