The Civil War clearly can be called this as there are many people who do call it that. Whether it should be called that is another matter altogether.
To argue that the war should be named in this way, you can say that the South was simply trying to protect its own way of life. This is clearly true. The South wanted to be left alone to govern itself as it saw fit. This was, in many ways, the same thing that the American colonies wanted at the time of the Revolutionary War.
However, when we call the Civil War the War for Southern Independence, we are implying that the war was in some way fought for a good cause. This is much harder to support. The basic right that the South was trying to preserve (at least in my view) was the right to have slaves. This is in no way an honorable or a just cause.
So, the war was clearly fought to allow the South to be independent. However, it was not fought for a noble cause (in my view). Therefore, it does not seem right to me to give it a name that implies that it was a “good war.”