From David Webb comes this suggestion, which I think beats all contenders, including my own "War of Union Ascendance," for the American conflagration in 1861–1865. He suggests "War of Involuntary Union."
Since this was not a civil war, a good name is essential to redirect thought and conceptualize it more accurately. His suggestion, like "War Between the States", equalizes the emphasis on both North and South. The word "involuntary" calls up "South" to one's mind and also suggests a contest of wills and arms, while Union calls to mind the forced outcome. "War Between the States" doesn't pinpoint these essentials of the conflict.