'Let us make us a name lest we be scattered."
Here, ‘a name’ means ‘a Shem’, which was equivalent to what Catholics understand as ‘a Pope’.
Shem was the first among his brothers, therefore the natural successor as the first among the leaders/fathers of humanity. A coup had happened a little earlier and humanity was in the midst of building a new social order. Now, they were trying to find a ‘Pope’ (which was really an anti-Pope) in order to stay united. It seems like Babel was being set up to be the capital of the ‘one’ world they were trying to make: One capital, one people, else, we will be scattered and end up with many capital cities…divided.
The God’s way was the natural family and trust from God no matter what. By this way, Noah was the father of humanity and therefore the natural (king). Naturally, he was to be replaced by his first born son (elder- to look over his little siblings, this order was always upheld among the people of God unless the elder was proved to be a coward in which case, the next in line in righteousness was chosen). Whatever happen, the one who was to be the elder for all human was to be a ‘first-born’ in righteousness. Obviously from the line of the first born. This is Shem and his descendants.
Shem also mean ‘Name’. The position of ‘first born’ meant also ‘priest’. And Shem being first of the fathers, he was for the whole humanity a ‘Pope’. He was the first among his brothers, meant to preside over them in love: primacy in love, (like the Pope in relation to other bishops and rest of Catholics.)
But people had been rebelling against God ever since Noah’s drunkenness, and its consequences on humanity. When, he scandalized his children and they took matters in their own hand (Can’t trust a drunkard). So Ham made a number of steps to take matters into his own hands. He installed his ‘first born son’ Canaan in the land of Shem (Salem) which was meant to be for the whole humanity what ‘Rome’ is to the Catholic Church. In the same inherited land of Shem, Nimrod (descendant of Shem) tried to make a ‘name’ (a Shem, a Pope) for the new ‘Church’ he was attempting to build.
Of course, this coup had not be recognized by Shem, nor Japhet (they had covered their father), but Noah, waking up too late, he could only curse (prophesy what was going to happen to) Canaan (son of Ham who had build a leadership behind his back). So they was still a ‘name’ (Shem) among descendant of Shem and Japhet. This caused the rebels to trying to make an other ‘name’ for themselves.
In religious terms, it is similar to what happen when there is scandal in the Church, and someone in attempt to repair, end up starting a denomination which will eventually be scattered into many denominations.
In secular terms, it is similar to building a United Nation to hold the world together in one accord (language), but this is really a distraction from human pride because God already made a United Nation which only can work, has worked, and will work: the Catholic Church.
Of course they failed. It is still from Shem that we have leadership in unity: belief in One God (monotheism) and also the new one humanity the Church.