so that we may make a name for ourselves
The desire of these city builders was to make a corporate name for themselves and by so doing to avoid the worries and anxieties of being scattered. This is the drive to empire evident in the work of Nimrod, and its sign and symbol is the city.
By and large in the OT, to know the name of something was to understand what it was and have dominion over it. Thus Adam receives the job of giving names to the animals (Gen 2:19). It also appears that names are given and received, not taken or made for oneself. God names the various parts of creation (Gen 1:5, 8, 10 etc). In 3:20 Adam names Eve; in 4:1 Eve names Cain; 4:26 Adam names Seth.
In Genesis 12:2 God promises Abraham, “I will make you into a great nation and I will bless you; I will make your name great, and you will be a blessing.’
Furthermore, it seems to be the preserve of God alone to ‘make a name for himself’ as in 2 Sam 7:23
“And who is like your people Israel– the one nation on earth that God went out to redeem as a people for himself, and to make a name for himself, and to perform great and awesome wonders by driving out nations and their gods from before your people, whom you redeemed from Egypt?”
Once again it may be that the idea at root here is that human beings are usurping something that belongs to God. They are making a name for themselves, rejecting whatever God may say about them or to them, and the means by which they will make a name for themselves is in the building of a city with a tower. There may also be an indication of their arrogance and conceit. They are seeking to storm heaven through their tower, and in order to preserve the name of God as pre-eminent in the cosmos, God must act.