I don’t really care what people call it, but the term “War Between the States” wasn’t all that common during the war itself. It didn’t really come into common use among Southerners until after the whole thing was over. If “Civil War” was good enough for Davis, Lee, and Forrest, you’d think it would be good enough for the UDC.
In some European countries, the common name is “War of Secession” (Guerra de Secesión, as the Spanish put it). Maybe we should start using it here in America; I think everybody could agree that “War of Secession” is pretty accurate.