I think one of the reasons the author chose not to name the character in "The Sniper" is to try and universalise the themes of war and emphasise the way that this civil war caught up so many people in it, not just individuals, but entire families, towns and cities. Note how the sniper is introduced:
On a rooftop near O'Connell Bridge, a Republican sniper lay watching. Beside him lay his rifle and over his shoulders was slung a pair of field glasses. His face was the face of a student, thin and ascetic, but his eyes had the cold gleam of the fanatic. They were deep and thoughtful, the eyes of a man who is used to looking at death.
I think it is important to note that the first piece of information we receive about this sniper is that he was a Republican, thus emphasising the side he was on and the way that Ireland was literally ripped in two by the Civil War. He is a universal figure by not being named, and thus his tragedy and the way it shows the horror of civil war is universalised.