Today marks the 150th anniversary of South Carolina's secession from the union, which marks the logical beginning of observances remembering the war that ensued. Naming that war, however, is very tricky because the common names used for it are biased for one side or the other. In order from extreme unionist to extreme Confederate, we can call it: War of the Rebellion, Civil War, War Between the States, War for Southern Independence, War of Northern Aggression.
In fact, it was a war between two nations (one of which was unrecognized by anyone else) known as the United States of America and the Confederate States of America. In terms of international law, the Confederate States of America was de facto an independent nation (meaning that it functioned as one), but was not de jure (meaning that it was not accepted as such by other nations. This would have been accomplished for the Confederacy if it had executed a treaty with Britain or France, or if it had signed its longed-for Treaty of Peace with the United States).
Technically, it was not a "civil war" because that term refers to a war for control of the national (federal) government. The Confederates did not want to take over the United States Government -- they just wanted a nation of their own.
The "War for Southern Independence" is perhaps the most accurate name, but seems to reflect a moderately strong pro-Confederate bias. "War of the Rebellion" is also technically accurate, but reflects a very strong pro-Northern bias. I usually call it the War between the States, which is technically incorrect, but is descriptive and mildly pro-Southern.
So, take your pick, and we'll know what your bias is. Or, we could start calling it the "War of 1861", which is completely neutral but not very descriptive.