WWII is called the Good War because it was a war that had the clear backing of the vast majority of the American public and because it was a war with a clear purpose that was obviously morally good.
In WWII, the US fought because we were attacked by the Japanese. This was clearly justifiable. We fought Germany in part because Nazism and fascism were so clearly evil. We were firmly on the side of good. Because of these factors, there was no real conflict over the war in the US. Everyone supported it and it brought the country together in a common purpose.
This is very different than subsequent wars. These wars have tended to be morally ambiguous and have lacked clear public support. For these reasons, WWII has come to be called "The Good War."