John Gill Commentary 1 Samuel 15:8

"And he took Agag the king of the Amalekites alive, and utterly destroyed all the people with the edge of the sword." — 1 Samuel 15:8 (ASV)

And he took Agag the king of the Amalekites alive
This name seems to be a common name of the kings of these people, as Pharaoh was of the Egyptians, see (Numbers 24:2) . When this king fell into the hands of Saul, he did not put him to death, as he should have done, but preserved him; for what reasons, see in the following verse:

and utterly destroyed all the people with the edge of the sword ;
that is, all that came in his way, or fell into his hands; all between Havilah and Shur; all excepting those that made their escape, for we after read of Amalekites, and that in large bodies, (1 Samuel 27:8) (30:1) .