As Sybil so adorably points out, Seymour Glass sounds a lot like "see more glass." Seymour sees more, presumably, than the rest of us can see. As we discuss in "What's Up with the Ending?", spirituality and Zen Buddhism were important concepts for Salinger. That he gives Seymour this special spiritual distinction is not surprising.
Speaking of Sybil, consider "Sybil Carpenter" as a name. In Ancient Greece, "sybils" were prophetesses, or female seers. They could predict the future. In this way, Sybil, too, sees more. She and Seymour are distinct from the story's other characters in that they are both spiritually advanced (especially in comparison to the materialistic adult women). Think also about the description of Sybil's shoulder blades as "winglike" (2.3)– this is no ordinary four-year-old. The last name "Carpenter" is also striking, as it brings to mind Jesus Christ, who was…a carpenter. We'll let you decide what to do with that.
"A Perfect Day for Bananafish" contains almost no exposition (straight-up telling) whatsoever. And yet we walk away from this story with a very good sense of its main characters (Seymour, Muriel, Sybil, even Mrs. Carpenter). That's because of Salinger's extraordinary dialogue – which takes up about 90% of the text.
Consider Muriel's conversation with her mother. We know that Muriel is materialistic, her mother protective, Seymour unstable, their marriage precarious and eccentric – all without any direct telling. The complexities in Seymour's dialogue with Sybil are similarly implicit. A single line of dialogue holds any number of important meanings (check out "Symbols, Imagery, Allegory" for a trove of examples).