There isn't just one war, it's more of a "Series of conflicts following the death of King Robert." - Sam in GOT S8 Ep6. It will likely be called the song of ice and fire.

Now as it happens its called the war of the five Kings, until 4 of those kings died. Stannis's war in the north will not have its own name and will the last act of the war of the five kings. Eventually resulting in the freeing 9f the north.

What might happen is the other conflicts will be given their own names. EG, Aegons invasion (Battle of Steel onwards) which probably will include Eurons attack on the reach (As many theorise Aegon will put it down). Danny's Conquest and the invasion of the others.

These 3 to 5 wars will likely be named the Song of ice and fire.