Actually, reference to "the civil war" predates the war itself as this was the commonly used phrase to describe and warn against what both sides saw to be approaching in the years before it. The feds officially called it the "War of the Rebellion," the confederates called it variations upon the "war of northern aggression" and the sort, and early post-war writers tended to refer to it as either the "civil war" or "war between the states." Civil war has been favored over all the others in recent times if for no other reason than that it is the easiest to say and shortest to write.
Or maybe because in 1902 Congress voted to adopt that name on all official documentation, replacing 'War of Southern Rebellion' and in place of the preferred southern 'War Between the States.'