This Abimelech was not the same that was in Abraham's days, Genesis 20:2-18, for this was near an hundred years after, but that was the common name of the Philistine kings, as Caesar of the Roman emperors.
Related Commentaries of Genesis 26:8
Genesis 26:8
8 And it came to pass, when he had been there a long time, that Abimelech king of the Philistines looked out at a window, and saw, and, behold, Isaac was sporting with Rebekah his wife.