The stated purpose of building a tower was to reach heaven and create a name for themselves in doing so. They wanted to be able to boast of their own strength in defeating the impossible. Satan had put it into their hearts to do such a thing rather than work on actually reaching God through works of righteousness.
I think that this angered the Lord because the people cared more about reaching heaven physically in order to make some kind of claim over what they did, when they didn't try to reach heaven in more spiritual ways like obeying God's commandments. Because of this, God confounded the language of the people so that they would be scattered.
Ether 1:33-43
The Jaredites from the Book of Mormon fit into the story of the Tower of Babel from the Bible because they were there at the same time this tower was being built. The language of the people was confounded, yet Jared asked his brother to pray to the Lord to ask and see if the Lord would spare them and their friends to keep their same language so that they would be able to communicate with each other. The Lord granted Jared his request and their language wasn't confounded.
Acts 4:12; Mosiah 3:17, 5:7-15; D&C 18:21-25
We can receive "a name" that can truly help us reach heaven through our Lord and Savior, Jesus Christ. We cannot receive salvation any other way than through Him. We must covenant with God that we will be obedient all the days of our lives through baptism. We must always "abound in good works" and come unto Him in repentance and humility; only then can Christ save us with His atoning sacrifice.
