“Babylon” is an early Christian code-word for Rome. It is used in many early Christian documents – for example, 1 Peter 5,12-14
12 I write you this briefly through Silvanus, whom I consider a faithful brother, exhorting you and testifying that this is the true grace of God. Remain firm in it. 13 The chosen one at Babylon sends you greeting, as does Mark, my son. 14 Greet one another with a loving kiss. Peace to all of you who are in Christ.
Clearly, “the chosen one at Bablyon” is the Church in Rome. In Revelations, John’s description of Babylon with seven hills makes it plain – the real Babylon was flat, and Rome is famous as the “City of Seven Hills.”
Rome in those days meant the Roman Empire, not the Church – which was a tiny sect persecuted by the authorities. Christians drew a parallel between the Babylonian Captivity of the Jews (in the 6th Century BC) and the rule of the Roman Empire, which held all people captive.
It would be hundreds of years before “Rome” would come to be synonimous with “Catholic Church.” Protestants who don’t know history like to pretend that a First Century Christian would mean the Catholic Church when referring “Rome,” but rather the Roman Empire.