Introduction
Eliphaz is a son of Esau and his wife Adah, named first among the Edomite chiefs in the genealogy of Genesis 36. His own son, Amalek, born to a secondary wife or concubine named Timna, is identified as the ancestor of the Amalekites, a people who become one of Israel's most persistent adversaries throughout the historical books of the Hebrew Bible.
Note: this Eliphaz, son of Esau, is a different figure from Eliphaz the Temanite, one of Job's three friends in the book of Job; the two share a name but are not identified with one another in either text.
Family
Family and Amalek
Genesis 36:12 records that Eliphaz had a concubine, Timna, by whom he fathered Amalek, alongside other sons by his primary household, making Eliphaz a significant hub in the genealogy of Edomite chiefs given in the chapter.
Descendants as Edomite chiefs
The genealogy in Genesis 36 lists several further descendants of Eliphaz as "chiefs" (allufim) of Edom, part of the chapter's extensive, formal record of the Edomite line descended from Esau, presented in a style similar to, though separate from, the tribal genealogies of Israel.