In The Road by Cormac McCarthy the names of the man and the boy are never revealed. Would this technically be considered a stylistic choice of the author? I pulled up a definition and it says "Style describes how the author describes events, objects, and ideas." Is the lack of names a style, or just a part of plot?
Omission is an extremely important part of style. Often what is said is actually less important than what is left unsaid, sometimes referred to as the subtext. Hence the critical importance of the oft-repeated advice to "read between the lines."
One particularly brilliant use of this stylistic device occurs in F. Scott's Fitzgerald description of Gatsby lying dead in his pool in chapter 8 of The Great Gatsby:
There was a faint, barely perceptible movement of water as the fresh flow from one end urged its way toward the drain at the other. With little ripples that were hardly the shadows of waves, the laden mattress moved irregularly down the pool. A small gust of wind that scarcely corrugated the surface was enough to disturb its accidental course with its accidental burden. The touch of a cluster of leaves revolved it slowly, tracing, like the leg of a compass, a thin red circle in the water.
Given that up to this point Gatsby's name has been heard in the novel far more than the man himself has been seen, this description, which carefully and deliberately skirts around the statement that "Gatsby was lying dead in the pool," is loaded with irony. This effect is accentuated by the banality of objects like a mattress and leaves and by the minimalism of words like "barely perceptible," "little ripples," "small gust," "accidental," and "slowly," which contrast starkly with Gatsby's bold, brash, fast-paced, intentional, and outsized lifestyle. The whole description is extremely fitting given the overall irony and complexity of Gatsby as a character whose grand self-created image is at odds with his true identity. Had Fitzgerald used the name "Gatsby" anywhere in this passage, this effect would have been lost.
Also, with regard to the example you give of the man and the boy in The Road, I think this is an extremely important stylistic choice by McCarthy that makes these characters universal, essential, even somewhat primordial. Though McCarthy develops these characters a lot in the novel, perhaps more important than their specific identities is their position as essentially the last man and the last boy on earth.
Wallace's answer is definitive, so this answer is merely in way of commentary on the issue.
- Hidden information is not only a stylistic choice, but a strategic choice
Viewed from the standpoint of information theory, meaning is created by an author's choices. In some cases author's want to "spell things out" in an unambiguous way, but great literature tends to leave as much as possible to the reader. In some sense, a poem or narrative is a puzzle. The author may be said to utilize game theory in determining how best to "hook" the reader and sustain interest over the course of the poem or narrative.
I wholeheartedly agree with Wallace that the omission of the characters' names by McCarthy is in service of universality and fundamentality of the characters. McCarthy's books are heavily allegorical, and The Road is distinctly a parable.
Another key omission on the Road that serves as a "hook" is the lack of explanation of exactly what the event was that ended civilization. As I recall, it was described simply as "three low concussions in the distance" [paraphrase] with no further explanation.