At the Choosing Ceremony, both Tris and Caleb were forced to choose the type of person they wanted to be; not an easy task, but one that was necessary for them to continue forward in this society. This choice will form their identity, and neither wants to be identified as the selfless and unassuming Abnegation they were for sixteen years of their lives. They both realize that in order to discover who they truly are, they have to leave their family behind. In an amplified way, this mirrors the choice every young adult must make when they leave adolescence. Even in a fantasy novel, the theme of adulthood looms large.
It is interesting to note that while both siblings chose to transfer, neither informed the other of their plans; in Tris's case, she assumed Caleb would never think of transferring from Abnegation, but what about Caleb? He clearly knew something was going on in Tris's mind when he told her she had to think of herself, so why didn't he say he was experiencing the same conflict? Did he not trust her enough to keep it to herself? Or is it just too risky as an Abnegation to talk about switching to Erudite? This says something about both Caleb's character and the nature of the feud between Abnegation and Erudite; both are more complex than we realize. This also communicates an inherent flaw in the society's design. The test results are meant to be secret, the first step towards indoctrinating the initiates into this society - a society ruled by "faction before blood". This sentiment is meant to strengthen the bonds within the factions, but often comes at the cost of one's familial ties. This idea will become fleshed out in later chapters.
In these chapters, Tris's character develops more as she begins to discover her true identity. The bravery required to leave her faction and switch to Dauntless is the first sign that she made the right decision, but she still has a lot more to prove. Her characterization continues to show through the various tasks she has to do before she even reaches the compound; jump onto the train, jump onto the building, and in particular, jump off of the building. That Tris was the first to do so speaks volumes about her determination and drive, and the reaction of the Dauntless at the bottom foreshadows that during initiation, Tris will be one to watch out for.
Then there's her decision to change her name: a name is the most central part of a person's identity, and most people typically do not get the luxury of choosing it for themselves. The name her parents chose for her, Beatrice, certainly suited her for the first phase of her life, but a modest and traditional name cannot continue to represent her as she moves into her new life in Dauntless. Because a name symbolizes identity more so than anything else, by choosing her own name, Tris chose her own identity—and it will be up to her to live up to it. Again, this idea of changing one's name signals the weakening of the family bond.
It is also necessary to take notice of the exchange between the initiates and the Amity boy, who says he won't jump because he would rather be factionless than dead. Tris disagrees, and this simple thought illustrates how ingrained the faction system is in these children; they are nothing without their faction. Faction before blood, plain and simple. Faction before everything. Are the factionless really as poor and misguided as Tris makes them out to be, or is that idea simply a way of brainwashing citizens into staying completely loyal to their factions - and to the system itself?
Lastly, Chapter 4 establishes the book's overarching villain - Jeanine Matthews. Whether or not what she says about Marcus Eaton is true, it's pretty clear that she's tying to stir up trouble and dissent between Abnegation and the other factions. Erudite's status as a faction of geniuses is used to gain power by spreading opinion - or propaganda - throughout the city. The truth is beside the point. The rift between the two factions is part of her larger plan, which will come to pass later in the novel.