When you see "theo," you know that you're dealing with a word that has something to do with God or gods. Just think of the word "theology." "Theo" comes from the Greek word "theos," which means "god." As a result, Theodore seems a fitting name for a boy so prepossessed with spirituality and God. The name "Theodore" is masked in this case by the diminutive and maybe even childish nickname "Teddy," which again is fitting – people miss out on Teddy's spiritual importance because of his young age.
If you read enough Salinger, you're bound to notice his painstaking attention to physical detail. If a character lights a cigarette, we know it, and we also know when he inhales, when he blows smoke, where he puts the ashtray, and when he puts his cigarette out. If he lights another one, the process starts all over again.
Critic Alfred Kazin writes that Salinger, by so carefully describing every detail of gesture, movement, and posture, "makes his stories hum, fills in every inch of the canvas with detail, not as a naturalist but as a dramatist wanting to make sure that his character walks just so upon the stage" (Source: Kazin, Alfred. "J.D. Salinger: Everybody's Favorite," from Contemporaries: Essays. Little, Brown: Boston, 1962.). We can easily identify this trademark Salinger-ism in "Teddy," in the very first paragraph:
He [Mr. McArdle] was speaking from the inside twin bed – the bed farther away from the porthole. Viciously, with more of a whimper than a sigh, he foot-pushed his top sheet clear of his ankles, as though any kind of coverlet was suddenly too much for his sunburned, debilitated-looking body to bear. He was lying supine, in just the trousers of his pajamas, a lighted cigarette in his right hand. His head was propped up just enough to rest uncomfortably, almost masochistically, against the very base of the headboard. His pillow and ashtray were both on the floor, between his and Mrs. McArdle's bed. Without raising his body, he reached out a nude, inflamed-pink, right arm and flicked his ashes in the general direction of the night table. (1.1)
After reading this passage, do you find that you've formed an opinion of Mr. McArdle? At the least, you probably have a minimum feel for the character or reaction to him. Salinger's characterization lies not only in the physical detail, but also in his specific word choice. Mr. McArdle moves his foot "viciously," he has a "sunburned, debilitated-looking body," he's "lying supine," he's resting "masochistically" as though he can't be bothered to make himself more comfortable, and he possesses a "nude, inflamed-pink, right arm." Salinger could just as easily have written: "Mr. McArdle was a slug-like man defined by his somewhat visceral physicality." But that doesn't seem to have the same effect, does it? With Salinger's way we get to see what Mr. McArdle is like. We see that he's grossly physical instead of being told that he is.
"Teddy" is largely a story of ideas; the bulk of the text is made up of Teddy's conversation with Nicholson, a conversation built around religion and philosophy. Teddy's ideas about death, God, education, reality, and perception are what most define his character. Who is Teddy? For the most part, Teddy's character IS this religious philosophy. Salinger just gave the theory brown eyes and shaggy hair. Similarly, Mr. McArdle is defined by his own exaggerated ideas of what is valuable (money and brand names, it would seem), and Nicholson, by his skepticism and (possibly) eventual acceptance of Teddy's propositions.