Short answers, pulled from the story.
The National Park Service uses the term Civil War to label its preserved battlefields across Virginia and Tennessee. The agency occasionally uses Southern names like Manassas and Shiloh for its battlefield parks located in those states.
Abraham Lincoln used the words Civil War in a message to Congress on the 26th of May 1862. Jefferson Davis wrote about the conflict using the same phrase in his own memoirs published after the war ended.
Segregationists coined the phrase War of Northern Aggression during the Jim Crow era of the 1950s. They attempted to equate contemporary efforts to end segregation with nineteenth-century efforts to abolish slavery.
Union forces frequently named battles for bodies of water or other natural features prominent on or near the battlefield. Confederates most often used the name of the nearest town or artificial landmark, making General naming conventions determined by the victor of each specific engagement.
Confederate brigades were frequently named after their commanding general like Hood's Brigade or Gordon's Brigade. Confederate batteries took names from towns or counties where they recruited, such as Fluvanna Artillery, while Union artillery batteries were generally named numerically.