The Capital of the empire was not moved from Rome to Byzantium. The imperial capital of the eastern part of the empire was moved from Nicomedia (in northwetern Turkey) to nearby Byzantium by Constantine I in 330 BC. The capital of the western part of the empire remained Milan.
Rome had ceased to be an imperial seat when Nicomedia and Milan were established as the imperial capitals of the two parts of the empire (286 BC) which were ruled by two co-emperos, one for each part. Rome became the nominal capital of the whole empire.
Byzantium was renamed Constantinople.