I don't think the soldiers themselves always had a name for a battle immediately after either. You'll see in many letters, diary entries, or reports written just after a battle they just refer to the date, e.g., "In the fight on Sept. 17." The official name(s) probably came along a bit later (weeks, months) as people started reflecting back on it and the word quickly spread.I think one of the things we are overlooking is who named them. Most civilians both North & South had no way to know that a battle was even going on, or much less a name until that got their hands on a newspaper or from the telegraph operator. The newspaper were just like the newspapers of today in that they wanted to sell papers.