Genesis 11 addresses the failures of human self-centeredness and points toward hope to build communities of blessed care.
Genesis 11 points forward to the ability for God to establish a name for the person(s) of God’s choosing in order that human flourishing and God’s blessedness can be given freely to all nations.
Genesis 11 establishes a subtle irony early in the story of the Bible about those who should seek to make a name for themselves whose names will not be recorded, set over against the many otherwise powerless persons (Shiphrah and Puah, Bezalel and Oholiab, Samuel, Esther, New Testament Disciples) whose names will be remembered in all nations for how God blesses them for their service to God’s purpose.
When the book of Genesis is taught, it seems a significant emphasis is given to Genesis 1-2, taken as though they are one story of Creation, Genesis 3 for the “so-called” Fall, Genesis 6-9 for the Flood story, Genesis 12, 15, 17, for covenants with Abraham, the binding of Isaac in Genesis 22 - and then perhaps some compilation of narrowing the chapter 13 story of Joseph into a single, simple story.
Genesis 11 does not come to the fore as most important in Genesis.
And yet, in Genesis 11 we have a kind of “hinge” for reading the book of Genesis.
Genesis 11 marks both continuity and shift in the story of Genesis.
Genesis 11 begins with a claim of unified language for the people (v.1). As a direct claim in the Bible, this presents a difficult connection to what comes in the preceding chapter, specifically at 10:5, 10:20, and 10:31 where the Biblical text notes the descendants of Noah and his sons having their own languages. The Bible text though, in this Primeval History, does not seem to be presenting a seamless linear and sequential history as much as it is focused on the larger role of God’s activity in and with creation and persons in God’s creation. What is most important in Genesis 11 is not any potential disparity with Genesis 10 and is instead what is happening with this particular community of persons who settle in the plain of Shinar (v. 2). 
As these inhabitants of this city gather, they engage in conversation with each other and determine to work together to make bricks. The NRSV translation: “Let us” (11:3 & again 11:4) work together might echo an attempt to think back to the “Let us” of God in Creation, purposing to create Humans (Genesis 1:26-27). The text of 11:3 begins with a phrase translated from Hebrew “and they said to one another” where the Hebrew literally has “a man said to his fellowman.” We have no named characters, only general “men.”
These persons want to work together though, it has been suggested, they are already outside of God’s purpose as they (1) attempt to build a name for their glory, not for the glory of God. And, (2) human persons have been told to flourish in creation, being fruitful and filling the earth (Genesis 1:28 to human persons in Creation and Genesis 9:1 to human persons of Noah’s descendants.) What humans have been told to rule over in all creation for all of God’s image to be extended through faithful service, the human persons instead narrowly focus their efforts and in service to God fail to extend God’s rule and, it seems, think they can reach to the heavens to directly subvert the Ruler they have been put into the world to serve.
11:4 notes that the human inhabitants want to build a city. While there is not yet any provision against cities in the Biblical text, the attentive reader has reason to wonder if this will not be a failed program. Cain and Abel (Genesis 4) were the first humans to live their lives fully outside of God’s protected place (The Garden - Genesis 2-3) and yet still in the handiwork of the Creation (all of creation is always the place of God’s sovereign rule). Not only does Cain’s offering (and/or attitude) not receive acceptance by God, when Cain is subject to the “mark” of God (Gen. 4:15) and forced further east (4:16), Cain and the first descendants of Cain’s lineage begin to build cities (4:17). As the attentive reader of Genesis 11 reads about what the people will do as the “us” of this story, they must wonder if the same repeating patterns of retributive violence and extended 77x fold curse (Gen. 4:15 and 4:24) will be extended into this narrative again in the plains of Shinar.
Ironically, they intend to reach the place of LORD (and undue God’s rule ?) as their tower will reach as high as the “heavens” (11:4) and yet, again with a note of distance from God and subtle ironic inversion, in order for God to fully see that which is supposed have a top reaching into his heavens, God has to “come down” to see that which these mere mortals are attempting to build (11:5). [It is important in this narrative that the LORD (YHWH) is the term used for God’s direct and immediate presence. See also the LORD in the immanent language of creation in Genesis 2:4bff and in the naming of God’s self to Moses Exodus 3 & 4].
In yet another level of irony, the individual “men” of 11:3 (“a man said to his fellowman”), the Biblical text has moved away from one Hebrew term for man as an individualized person (The Hebrew ish) to another term for humankind as a collective as humankind (The Hebrew term is ha’adam). Instead of the reader meeting on an individual level the “men” with their “names” who are building a city and tower to establish their names, the narrative demonstrates the smallness of that which they are building as the LORD must come down to see it and yet further the smallness of their task as they are a collective whole and no one is worthy to be named as they’re all part of the mass of humankind (ha’adam).
11:6-7 allow the reader into the “mind” of God as we hear the LORD speak to God’s self and the “Let us” of God (see also Genesis 1:26ff). In 11:6 the LORD notes they are one “people” (Hebrew ‘am - distinct from the “man” or “humankind” they had been before).
In 11:6-7, the LORD announces that a forced mixing and mingling (commonly translated “confusion”) of their language will be forced upon them. 11:8 notes that the mixing of their languages, by the force of the LORD’s doing for has left them “scattered.” The self-same thing they had hoped to avoid (11:4), being scattered, is now forced upon them by the LORD’s direction action (11:8). They did not want to be scattered and they did want a name, and they are scattered and we know none of their names.
The forced dispersion, and the derision of their being forced out as “Babel” has overarching concerns here and elsewhere in the Bible. Some have pointed to the “babel” as the kind of “babbling” sound that a baby makes. These “men” had wanted to be builder and their common language is reduced to a term that could be seen as one of derision, they only “babble” like children at Babel. A place they hoped would set them apart for their pre-eminent coming together to build a name, and yet they “babble” off without a single name being recounted except for their babbling so called “Tower of Babel” (It is important to note that the Bible never calls their tower the Tower of Babel - only the place and the babbling persons as having been at Babel after the dispersion. Babel, then, is the name of derision for their dispersion.)
In the plain of Shinar, the people had come to build a name for themselves, with a tower, and by the end of this brief narrative, (11:8-9), they are scattered and we know not a single name of not a single one.
What humans by their self-serving hubris and pride had sought to establish for themselves, separate from God’s purpose, remains but the shell of a building (we must imagine) left to decay in the sands of time. 
Three other lines must be noted.
Where the Biblical text narrates that these people on the plain of Shinar had intended to build a name for themselves, the next verse Scripture begins with the genealogy of a people who do have a name! Genesis 11:10 read “These are the descendants of Shem” though in the Biblical text Shem means “name.” In the Bible, in yet another irony from what is read in Genesis 11:1-9, a genealogy of a people who have a name, beginning with a person named “Name” (Shem 11:10) immediately follows the inability for a people to have made a “name” (11:4) for themselves. The irony is intentional.
Yet further, the One who “gets a name” (see Genesis 12:1-3 and especially Genesis 12:2 where God promises a name to Abram) ) at the end of the genealogy of those who have a Name, is a man who has only his barren and childless wife (11:30). The LORD can give names to a single man and single woman, if the LORD wills, and not to self-serving men and their fellowmen who are outside of God’s purpose. Their frutiful building campaign is brought to naught, and through the barren couple God will establish a name that is still announced through nations the world over, through the descendants of Abra(ha)m!
And still yet further, while this text is far removed in the Bible from the New Testament and what happens in the world after the ascension of Jesus, it does seem to be in the purview of the book of Acts that a “new name” is given that unites persons. Acts 2 can be read is a kind of reversal of Babel where distinct people of diverse languages while remaining in their language groups, now have a name that unites them, that new name forms a new genealogical bound for all who embrace it and are baptized into it as Peter proclaims that it is in the “name of Jesus” (Acts 2:38) that a new unity emerges and salvation is extended for “all who are far off” having been scattered, it seems, since the time of Babel.
 The plain of Shinar may be a reference only to the descendants of Noah’s sons via Ham, as Nimrod is said to have occupied this territory (10:8-10).
 An apt modern poetic discernment of the idea of attempting to build a name for oneself and yet being forgotten is certainly found most eloquently and succinctly in Percy Shelley’s poem Ozymandias. See http://courses.wcupa.edu/fletcher/britlitweb/bklinea.htm