Saul went along one side of the mountain and David and his men went along the other side. Even though David was hurrying to get away from Saul, Saul and his men were closing in on David and his men to capture them.
Then a messenger came to Saul saying, "Come quickly, because the Philistines have raided the land!"
So Saul broke off his pursuit of David and went to engage the Philistines. Therefore, that place was named the Rock of Separation.