🔼The name Amalek in the Bible
The name Amalek is assigned to a few people in the Bible, but it isn't clear how many different Amaleks there are: The fist Amalek to appear is a son of Eliphaz, a son of Esau, the son of Isaac and Rebekah and the brother of Jacob. This Amalek's mother is called Timna and his grandmother is Adah (Genesis 36:12), and he becomes a chief in Edom (v16).
But even though this is the first Amalek to be called by name, there probably was one before him. During the war of Four against Five Kings, a people called the Amalekites is mentioned conquered by the Tetrad Coalition of kings Amraphel, Arioch, Chedorlaomer and Tidal (Genesis 14:7), but it isn't clear whether they were called Amalekites because they descended from a man named Amalek or simply lived in a town or region called that way.
In his fourth oracle, the prophet Balaam proclaims Amalek to have been the "first" of the nations, but it isn't clear if he means Amalek's prominence or earliness (Numbers 24:20), or even whether he means the descendants of Esau or the Amalekites who were first trounced by the four kings.
🔼Etymology of the name Amalek
The word עמלק does not really exist, and BDB Theological Dictionary dares not to propose an interpretation. But, says Jones' Dictionary of Old Testament Proper Names, as a name it may be a compound of the Hebrew word עם ('am), people or nation, from the assumed root עמם:
Jones further proposes that the second part of the name Amalek comes from the Hebrew verb לקק (laqaq), lap or lick:
The second part of the name Amalek may also have something to do with the Hebrew verb מלק (malaq), meaning to nip:
The Amalekites were thus either known as the Nippers or as the Lickers. Perhaps little Amalek when he was born licked more frequently than others, and was named Leq and his people Am-aleq, which then was projected back on their arch father. Or perhaps, since the Amalekites were a bitter enemy of Israel, the descendants of some guy who in retrospect came to be known as Amalek, were known as either the Wrung Off People, or the People That Wring.