Names can tell us a lot about a person, sure, but naming can tell us a great deal, too.
Archie names things around him that aren't usually given names, like Señor Saguaro. Archie has a fondness for inanimate objects, and he fully expects people to share in that fondness. He talks to Señor Saguaro, and wants his visitors to talk to the cactus, too. It's a way of personifying the plant, giving him human traits so that Archie can have another friend (as if he needs one).
Archie also names the prehistoric skull of a rodent Barney. To give a name to something long, long, long, long dead, is a bit unusual, but not for a man who names cacti. Nevertheless, it tells us a bit more about our Archie. He seems to think that even long dead things have something to say to us, if only we pay attention. By giving Barney and Señor Saguaro names, he boosts their value to his visitors. He makes his students pay attention to things they might have otherwise overlooked.
Plus, there's the fact that Stargirl names herself. What kind of name is Stargirl, and how in the world does she come up with it? She tells us she was "walking in the desert one night, looking up at the sky […] and it just sort of came to [her]" (13.26). In a way, both her name, and her act of naming herself tell us that Stargirl is a free spirit. She won't be defined by any name that another person might give her, and when she chooses her name, it's just kooky enough, and just profound enough, to reveal her true self to those around her.