The tower is used to called the Christea Turris (Tower of Christ) by the Genoese and the Megalos Pyrgos (The Great Tower) by the Byzantines.
Actually it wasn't the first tower in Constantinople as it was built to replace the Old Tower of Galata (Megalos Pyrgos / Great Tower) which controlled the northern end of the huge sea chain that closed the entrance to the Golden Horn Bay (Haliç).