What is the ambition and fear described at Gen 11:4 that they wished to build a “tower” with a “top…unto heaven,” to “make a name” in order to prevent being “scattered” over “the whole earth”?

To begin with the ambition. In a few places in the Bible, intimidating cities are described in a way reminiscent of these plans for Babel: for example, the cities of the doomed Amorites “are great and walled up to heaven” (Deut 1:28), while the “high-walled fortress” of Moab “will be brought down” (Isa 26:12). As to making a name for them, this means attaining a measure of earthly glory, similar to those “mighty men which were of old, men of renown” (Gen 6:4), or to David who “gat him a name” after smiting “the Syrians in the valley of salt” (2 Sam 8:13). Here, of course, the monument will be, like the pyramids of Egypt, a supposedly-lasting testimony to the power of the king who builds it. As to being “scattered,” part of the thing to be feared here is the peril of diminished numbers, when different camps might begin to wage war on each other. There is another sense in which being “scattered” would be a curse: God said that if the Israelites follow the gods of the idolatrous Canaanites, “the Lord shall scatter you among the nations” (Deut 4:27), which indeed is precisely what happened later on in the history of Israel.