During the "Civil War" there were many terms used by both sides, including "The War Between the States" and "The War of Northern Aggression," and some we don't want to repeat.
Anything you call it will be revised in 20 years as politics and political correctness changes American language.
To me, it is the (capitalized) Civil War, and I'm not sure how you deliniate that from the Civil War in Spain in the 1930's or any of the myriad Civil Wars since recorded time began.
rsl