Stephan, I've used most of those different terms. I most like War Between the States, though it is inaccurate. I use Civil War, only because it's short and known, and almost always in the context of criticizing it. I like War of Southern Independence or War to Prevent Southern Independence, but sometimes it turns people off – not that it should, but it makes it harder to explain some things to them.
I've finally settled on my favorite term for it: Lincoln's War. Short and to the point. Hardly inaccurate, as far as I can see.