When Hahp first sees Gerrard, he assumes he's some kind of messenger boy or whatever:
He wore rough-woven clothes from some South End market stall. Sweat had plastered his dark curls against his scalp. When he stood up, he gawped at the carriages that were now alighting on the huge stone wall. Messengers were street boys, always. No one else was hungry enough to accept a few coppers to climb the endless stairs. (6.9)
It's a mystery as to how he learned to read, or how he managed to get on the wizards' radar as someone worth admitting to the academy. Clearly he's not a noble kid disguising himself as a beggar for kicks, since he doesn't even understand how to get water out of a sink: "What son of any important family, anywhere in the wide world, could not work a simple water faucet?" (16.9). This makes him pretty exceptional at the academy.
We get a clue as to where Gerrard is from when (however many years earlier) Sadima gets directions to the house where Somiss and Franklin live in Limòri. It's on the corner of two streets: da Masi and Market (17.9). Maybe if Gerrard really is a street urchin, da Masi is the street where he was found as a baby, or where he grew up? We're not really clear on the naming conventions of beggars in this particular fantasy setting, but it seems like a possible connection.
When Gerrard and Hahp actually start to talk to each other, we learn a bit more about Gerrard's life. He grew up in the South End of Limòri, without a family: "I didn't know who my mother was, much less my father" (34.22). In other words, he's an orphan.
Basic stuff that Hahp takes for granted—like having a beloved childhood toy to imagine and manifest using the magic stone—wasn't in Gerrard's life. He says: "It isn't fair… I didn't have a toy" (34.14). Poor kid. Hahp takes pity on him and helps him out, and it looks like Gerrard is almost too proud to accept the help. Same deal with soap—when Hahp makes soap for himself, it doesn't even occur to him that Gerrard might not have had much experience with soap due to his background.
Hahp is so spoiled that he starts to get on Gerrard's nerves. Gerrard cuts off Hahp one time while he's talking and says: "You don't know anything about me, you spoiled little s***" (24.16). Clearly something touched a nerve, and it's a little bit satisfying to have the kid Hahp dubbed Fishboy shut him up.
Gerrard is stubborn and smart, and by golly he doesn't want to die. Upon entering the academy, he immediately begins to try to memorize the winding tunnels. Once Hahp understands this, he grudgingly admits: "He wasn't crazy, he was smart" (10.9).
Gerrard knows that only one student will become a wizard, and he wants it to be him. Because he's used to hunger, he doesn't mind studying on an empty stomach, so his lowly background is almost a plus in these situations. For most of the story, whenever Hahp tries to reach out, Gerrard reminds him that he's determined to succeed. We get gems like this from Gerrard: "If I have to beat you senseless so I can study, I will" (18.30). That's one way to talk to your roommate…
He tends to keep his distance from the other boys, possibly because of the distance in social class, and possibly because he's resolved to make it on his own. Hahp observes Gerrard at one point standing "a little apart as usual. His face was rigid and his arms were folded. He did not look scared and desperate, and I hated him for it" (26.6). Gerrard has likely survived in crummy situations before, and so he knows he can make it through.
By the end of the book, though, he has his doubts. He says, "I have to graduate. I have to" (64.13), but then he also admits, "I can't move my thoughts. I can't make anything but fish stew" (64.15). That's when he and Hahp make a pact to secretly help each other. Even though Gerrard is really driven to succeed, he realizes that he needs help to have a shot at graduating and then getting revenge on the wizards. And now maybe, just maybe, he actually has a shot at it.