Charles Ellicott Commentary Esther 3:1

"After these things did king Ahasuerus promote Haman the son of Hammedatha the Agagite, and advanced him, and set his seat above all the princes that were with him." — Esther 3:1 (ASV)

Haman ... the Agagite. —Nothing appears to be known about Haman except from this book. His name, as well as that of his father and his sons, is Persian. It is therefore difficult to understand the meaning of the name Agagite.

This name has generally been assumed to imply descent from Agag, king of the Amalekites, with whom the name Agag may have been dynastic (Numbers 24:7; 1 Samuel 15:8). Thus, Josephus (Ant. xi. 6.5) and the Chaldee Targum call him an Amalekite.

But apart from the difficulty of his name being Persian, it is hard to see how, after the wholesale destruction of Amalek recorded in 1 Samuel 15:0, any members of the royal family could have remained, maintaining a distinct tribal name for so many centuries. In one of the Greek Apocryphal additions to Esther , Haman is called a Macedonian.