The stated purpose of the tower that was being built by the people of the world was to reach heaven. More specifically it was men trying to cheat their way through this life and not have to go through the trials that are a part of the learning process.
This desire that they had to reach heaven was not righteous. They aspired to obtain the things of heaven through their own knowledge and their own will. They determined that they knew better than God and it was this idea that they were independent of him that they didn't need his help. It was their unrighteous desires which caused him to change their language. In order to scatter the people he changed their languages. Not only does that make it so they were unable to finish building their tower but it made it so the basic connections of families and friends were separated. I imagine that the separation of languages caused the people to seek out those who they could understand.
The Brother of Jared lived during this time which the world was incredibly wicked instead however he was a man that knew God and prayed to be allowed to be able to speak with his family and friends. The lord allowed that those people with him to be able to communicate with each other because of their righteousness.
The people of the earth when they were building the tower to reach heaven were trying to gain a name unto themselves. This was their attempt to avoid using the plan of salvation. It was the same idea that Lucifer had in heaven. That the glory be his and not Gods. These people wanted to do the same.
What truly allows us to have a name is taking upon us the name of Christ, through baptism and through doing good works continually.
