Babylon the Great may have been built somewhere near the location of the tower of Babel, but it was built centuries after the destruction of that tower and the only thing they had in common was the root word in their respective names. Babylon was built by King Nebuchadnezzar according to the scriptural account, and somewhere around the reign of King Hezekiah, fairly late in the biblical narrative.
Babel that later came to be called Babylon was built by Nimrod, for Genesis 10 says: "Cush became father to Nimʹrod. He was the first to become a mighty one on the earth. He became a mighty hunter in opposition to Jehovah. That is why there is a saying: “Just like Nimʹrod, a mighty hunter in opposition to Jehovah.” The beginning of his kingdom was Baʹbel, Eʹrech, Acʹcad, and Calʹneh, in the land of Shiʹnar."(Gen 10:8-10)
The name Babel is derived from the verb ba·lal´, meaning “confuse.” Local citizens, thinking of their city as God’s seat of government, claimed that the name was compounded from Bab (Gate) and ilu (God), signifying “Gate of God" or Babylon.
At Genesis 11:1, it establishes that "all the earth continued to be of one language and of one set of words", before Jehovah God caused "confusion" of the people, being divided into different groups due to the new languages that they now only knew, having no clue as to what the previous language of most likely Hebrew meant.(Gen 11:5-9)
Babel’s God-defying program centered around construction of a religious tower “with its top in the heavens.” It was not built for the worship and praise of Jehovah, but was dedicated to false man-made religion, with a motive of making a “celebrated name” for the builders.(Gen 11:4)
The approximate time of such building may be drawn from the following information: Peleg lived from 2269 to 2030 B.C.E. His name meant “Division,” for “in his lifetime the earth [that is, “earth’s population”] was divided”, in which Jehovah “scattered them from there over all the surface of the earth.” (Gen 10:25; 11:9) A text of Skarkalisharri, king of Agade (Accad) in patriarchal times (who appears to have reigned c. 2153–2129 B.C.E.?), mentions his
restoring a temple-tower at Babylon, implying that such a structure existed
prior to his reign.
Nimrod, who lived in the latter part of the third millennium B.C.E., founded Babylon as the capital of man’s first political empire, in which later generations of rebuilders came and went. The
Encyclopedia Britannica says of Hammurabi, that "Hammurapi, (born, Babylon [now in Iraq]—died c. 1750 bce), sixth and best-known ruler of the 1st (Amorite) dynasty of Babylon (reigning c. 1792–1750 bce), noted for his surviving set of laws."
So, long before Nebuchanezzar II lived (reigned 625-582 B.C.E.) were a long list of previous rulers (such as his father Nabopolassar [reigned 645-625 B.C.E.] who founded a new Babylonian dynasty as well as Babylonian King Merodach, who sent a gift to Hezekiah [reigned 746-717 B.C.E.] when he had heard he had been sick, Isa 39:1), that continued to "remodel" ancient Babylon till its total demise by the 4th century C.E.(Isa 13:19-22; Note: King Nebuchadnezzar II created "the hanging gardens of Babylon", considered one of the seven wonders of the world, and said presumptuously: "Is this not Babylon the Great that I myself have built for the royal house by my own strength and might and for the glory of my majesty"(Dan 4:30), so that Jehovah caused him to become insane for seven years, Dan 4:25, 33)
Now down to Babylon the Great, that it was named after ancient Babylon as a center of false religion by Jehovah God in the Bible book of Revelation. Those who do as Jesus said, to "get the sense of it" (meaning of the Greek word
syniemi that he used some six times at Matthew 13, and that literally means "to mentally put the pieces together") concerning God's Kingdom, that these ones can figure out reasonably, by doing serious research and meditation without bias, that ancient Babylon was the prototype of Babylon the Great.
Of course, a person has to recognize what is "truth" and what is "lies" for them to be able to discern the deep meaning of Babylon the Great, to sort out "fact from fiction".