One of reasons Crane does not name all his characers is because a primary theme of "The Red Badge of Courage" is the anonymity of war, or how the individual is lost in the machinery of combat. In the opening pages of Section 1, Crane speaks of the army unit as an entity unto itself, telling the reader that "the army awakened", and that "the army might start on the march". The names of the characters who make up the unit are not important, just as the individual himself is not important once he has surrendered himself to the inexorable machine.
"The Red Badge of Courage", as a naturalistic work, focuses on the powerlessness of men in the face of nature and outside forces. Man is insignificant, so it really doesn't much matter who a person is in the greater scheme of things. Especially in combat, Crane is saying that individuals have little choice in how they conduct themselves. Although their goals and aspirations may be lofty at first, once they are "part of (the) blue demonstration" (Section 2), they pretty much end up either doing what they are told, or what everyone else is doing. As Jim Conklin, one of the few named characters observes, "if a whole lot of boys started and run, why, I s'pose I'd start and run...but is everybody was a-standing and a-fighting, why, I'd stand and fight" (Section 1).
The main reason is that in war, you really don't know everyone's name, because it is just such a huge mass of people. It makes the book more realistic, because of the afore mentioned reason.