Because significant battles or even wars tend not to get specific unique names except in retrospect when it has to be clarified what battle or war is being referred to.
Example: until sometime after 1939, World War One wasn't called the First World War, World War One, or anything. It was simply The Great War. It was only when a similar conflict arose that people felt the need to be more specific. "Great War" was quite sufficient.
Other times, the battle is considered so iconic that there's no need to get more specific about the battle because everyone knows the one battle that is being referred to.
Another example: the Battle of Britain. The Battle of the Atlantic. There's been many battles that have taken place in Britain, many that have taken place in the Atlantic Ocean. Yet when you mention those two battles, it's understood you are talking about the Luftwaffe vs RAF in 1940, and the Allies vs the Germans in 1939 to 1945.
This is despite the fact that in 1914-1918 it was the same combatants in the same areas, fighting similar conflicts. Doesn't matter, they only refer to World War 2.
Others: Battle of the Pass (sometimes the Battle of the Defile, depending on how the Arabic is translated). Battle of the Frontiers. The Night Attack. Battle of the Ironclads. Battle of the Iron Bridge. Lots of battles have taken place in mountain passes, on frontiers, at night, between armoured ships, and at bridges made of iron. Yet those names all refer to specific battles.
So the Battle of the Binary Stars, as the first battle of the war, gets first dibs on the name. There may be other battles in other binary systems, but they get other names. When someone mentions The Battle of the Binary Stars, everyone knows what battle is being referred to.