The English name of ancient Mesopotamian city is Babylon. However, the name of tower is The Tower of Babel. Is there a difference between Babylon and Babel? Why aren't the words identical?
Babel and Babylon have different origins and may actually reflect different words.
The city known as Babylon was founded circa 2334 BCE, around or before the reign of Sargon of Akkad. Akkadian was the native language of the Mesopotamian nations at that time.
The city became the largest in the world and the center of power under Hammurabi (1792-1750 BCE). The complete history of the place name is disputed. Hammurabi called his realm Babylonia (a transliteration of what is represented as Bab-ili, Babilli, or Babilla, from Akkadian (or perhaps Old Babylonian, which was the language of king Hammurabi). The English Babylon comes from Greek Babylṓn (Βαβυλών), from that transliteration.
Bāb-ili ("Gate of God" or "Gateway of the God") also corresponds with the Aramaic Bab for Gate and El for God, hence Babel. In the Bible, the place name appears as Babel (Hebrew: בָּבֶל).
The Mesopotamians built many monumental towers as temples. Archaeologists have discovered nineteen of these buildings in sixteen cities; the existence of another ten is known from literary sources. The ancient Babylonians called these brick mountains a ziqqurratu or ziggurat, which can be translated as "rising building" (Akkadian zaqâru, "to rise high").
Babylon, itself, contained a number of these. The Etemenanki was among the largest (92 x 92 x 92 meters). It was the most important (its Sumerian name E-temen-an-ki means "House of the foundation of heaven on earth"). This temple tower was erected at what was thought to be the center of the world, the axis of the universe, where a straight line connected earth and heaven. This aspect of Babylonian cosmology is echoed in the Biblical story, where the builders say "let us build a tower whose top may reach unto heaven" (apparently heaven is at 92 meters).
This is the tower known as the Tower of Babel. Construction of the tower took over a century. The tower must have looked unfinished for a long time, and this may explain how the Biblical story came into being.
The name "Tower of Babel" came from the biblical story about the tower, it was not the actual name of the tower (Etemenanki). Babel is a transliteration of the Hebrew. It could mean the Hebrew equivalent of the "Tower of Babylon". Or as Eike Pierstorff writes, it may have been a play on words. It could tie into the Biblical story because Babel is similar to Balal (בלל), the Hebrew word for confusion, and the verb bilbél (בלבל), "to confuse".
Addendum: Incidentally, there is no connection between "Babel" and "babble", even though it might seem like the obvious origin. From Online Etymology Dictionary:
mid-13c., babeln "to prattle, utter words indistinctly, talk like a baby," akin to other Western European words for stammering and prattling (Swedish babbla, Old French babillier, etc.) attested from the same era (some of which probably were borrowed from others), all probably ultimately imitative of baby-talk (compare Latin babulus "babbler," Greek barbaros "non-Greek-speaking"). "No direct connexion with Babel can be traced; though association with that may have affected the senses" [OED]. Meaning "to talk excessively" is attested from c. 1500.
c. 1500, "idle talk," from babble (v.). In 16c., commonly in reduplicated form bibble-babble. Meaning "inarticulate speech" is from 1660s. Other nouns meaning "idle talk" included babblery (1530s), babblement (1640s).
Babel is the Hebrew name in biblical myth; since "Tower of Babel" is taken from scripture the Hebrew name is used. If I interpret the Wikipedia entry correctly is a sort of pun with an Hebrew word for confusion:
In the Bible, the name appears as Babel (Hebrew: בָּבֶל, Bavel, Tib. בָּבֶל, Bāvel; Syriac: ܒܒܠ, Bāwēl), interpreted in the Hebrew Scriptures' Book of Genesis to mean "confusion", from the verb bilbél (בלבל, "to confuse")
In contrast "Babylon" is (the transliteration of) the places name (as per Wikipedia, "Greek Babylṓn (Βαβυλών), [is] a transliteration of the Akkadian Babili]") , so that is used when talking about geography instead of mythical stories.