When constantine rebuilt byzantium it was called new Rome because

Constantine was making his own capital city in monumental fashion, but wanted to give it also the prestige and aura of the Roman Empire. The building of Constantinople took several years, and Constantine modeled it after Rome, with government buildings designed in Roman style. The existing city of Byzantium was the place Constantine built up and renamed after himself as Constantinople. (That's why the Eastern Roman Empire often is referred to as the Byzantine Empire.) Today, Istanbul is the name of the city that was once Byzantium and then Constantinople