Short answers, pulled from the story.
Byzantium was founded by Byzas of Megara, a Greek city-state near Athens, with the date most commonly given as 667 BCE based on the authority of Herodotus. Eusebius, writing centuries later, placed the founding at 656 BCE. Ancient legend identifies Byzas as the city's official founder, or oikistes.
Constantine I refounded Byzantium in 330 CE as an imperial residence modeled on Rome, calling it Nova Roma. The city came to be known as Constantinople, meaning "city of Constantine" in Greek, reflecting his role as its refounding emperor and patron.
The star and crescent were symbols of the goddess Hecate, to whom the Byzantines attributed their survival when a bright light appeared in the sky and thwarted a surprise night attack by Philip of Macedon in 340 BCE. Byzantine coins from the 1st century BCE show a crescent with an eight-rayed star on the reverse, and the motif was associated with the city by the late Hellenistic or early Roman period.
Istanbul derives from the Greek phrase meaning "to the city." Ottoman Turks used the name after conquering Constantinople on the 29th of May 1453, though it was not officially renamed Istanbul until 1930.
The historian Hieronymus Wolf introduced the term "Byzantium" to describe the eastern Roman Empire in 1555, a century after the empire had ceased to exist. The people of the empire itself called their state the Roman Empire, using the Greek phrase Basileia ton Rhomaion.
Bezant, also spelled besant or byzant, is an English term for a gold Byzantine coin. It derives from the Old French besan, itself drawn from the Latin Byzantinus applied to Byzantine coinage from the 9th century onward. The English usage dates from the 12th century.