We know that names are important from the very first chapter of the book, when Miss Rosa says, "He wasn't a gentleman. […] He came here with a horse and two pistols and a name which nobody had heard before […]." (1.10). In other words, Sutpen's name identifies him as an outside: he's not a Coldfield or a Compson, the two big names in Jefferson. And for all the disdain the locals feel for him, they are obsessed with his name, as we soon find out (from that wily omniscient narrator): "[…] the stranger's name went back and forth among the places of business and of idleness among the residences in steady strophe and antistrophe. Sutpen. Sutpen, Sutpen. Sutpen. Sutpen" (2.1).
Specific names also hold specific meanings. There are plenty of examples, but one in particular stands out: Charles Bon. Charles is a pretty regal name and "bon" means "good" in French. Basically, Sutpen names his child – whom he originally believes will be heir to his dynasty – Charles the Good. This is particularly noticeable because Sutpen refers to the other people in Haiti with generic names like "the planter" and "the wife." Charles Bon must be something special. And he sure is.
We're just going to throw a few bullet points your way:
Although Faulkner suggests that there are several Southern identities, everyone from the South – even those born after the Civil War – is bound by its violent history.
Social status cannot be discussed without reference to race in Absalom, Absalom! The novel suggests that the whiter a character looks, the higher he or she is in social status. For example, Charles Bon can "pass" and live the life of a gentleman, but Jim Bond (the heir to the Sutpen fortune) has darker skin and basically lives like a beast.
But early on, when a slave sends him to the servant's entrance of the Pettibone mansion, Sutpen finds out that whiteness alone doesn't guarantee status. When he arrives in Jefferson without "a name" (status), the townspeople reject him. Seeking "the shield of a virtuous woman" (1.10), Sutpen climbs the social ladder by marrying into the Coldfield family. Social status is not just about getting more money than Pettibone – it's also about being part of an established family and having a reputable means of earning wealth. (As in owning slaves rather than ripping off American Indians – but that's another story.)