The phrases "Let's build a city", "Let's make a name" express an attitude of defiance and rebellion against God, as well as an excessive ambition. The project had, certainly, a bad start. It was an entirely human enterprise, and its promoters were designed to enlarge man to the point of becoming independent from the Creator.
The Bible is clear in its warnings against the attitude of acting in that way, when human beings turn their backs on God, pretending to build a future for themselves, totally detached or separated from God.