Successor to what, exactly?
You would have to ask Him yourself, we are not that close. But rest assured when I meet Him face to face your question will not be one of the first I ask. Geography was never a great interest to me.
Are you talking about the book of Revelation?
Well, in many parts of the Bible, ‘Babylon’ is used as a ‘code-name’, in a way, for Rome.
Babylon was the major power in the region during the later OT period, when Judah was defeated and sent into exile. Since Rome was the superpower of the region during the New Testament era, it was sort of the comparable state/city to Babylon.
Both were (to the faithful) godless, corrupt and decadent societies. Both were arbitrary in their control over God’s people, becoming increasingly dictatorial and cruel.
Since Babylon had become the “type” for the imperial, persecuting power, it became a stand-in for the Selucids under Antiochius V Epiphanes, and later for Rome after the early persecutions, especially under Nero.