Alice C. Linsley
When I was in seminary, my Old Testament professor told the class that he doubted Isaac’s existence because there is so little information about Isaac. He noted that the story of Isaac pretending that Rebecca was his sister parallels the story of Abraham asking Sarah to say that she is his sister. He concluded that Isaac is a literary construction reflecting the author’s love of doublets. Doublets are duplicate narratives of the same event, which source critics believe is a single story told by two different authors.
My professor also noted the limited genealogical information about Isaac (Yitzak). He is presented as an only son after his half-brother Ishmael was sent away. He has only one wife, unlike his ancestors, and she is barren until God hears Isaac's prayers and she conceives twins.
While I appreciate this professor’s observations, I disagree with his conclusion. Isaac’s historicity can be verified by his adherence to the kinship pattern of his ancestors. We don't find kinship patterns as complex as this surrounding fictional characters. Further, the kinship pattern of Abraham's people reveals a good deal of information about the principle figures of Genesis.
We note that after the binding of Isaac, Abraham and Isaac are found living in Beersheba and it was to Beersheba in the south (Gen. 24:62) that Abraham’s servant brought Rebecca to meet her betrothed. Beersheba was the settlement of Abraham’s wife Keturah. Had Isaac married a half-sister or a cousin other than Rebecca, he would have married someone from the line of Abraham by Keturah. The evidence points to him marrying a daughter of Yishbak. Yishbak was one of Abraham's sons by Keturah.
The evidence for Isaac’s other wife is rather hidden, as is the identity of Abraham’s mother. The final editors of Genesis wanted to preserve the claim of Isaac as the son of promise through whom Israel would claim the Land. It wouldn’t do to admit that Isaac had other children by an Arabian wife of the house of Sheba, or that Abraham’s mother was Canaanite. Yet the kinship pattern of Genesis provides the essential information to draw these conclusions and to justify them on the basis of the text alone.
It is likely that Isaac had other sons and daughters besides Jacob and Esau. It is possible to trace them through the cousin bride’s naming prerogative. Rebecca’s father was Bethuel (Gen. 22:23), a son of Na’Hor, Abraham’s brother. Why didn’t she name her first-born son Bethuel after her father? This is the pattern for those who were to rule. We are given this explanation: Jacob grasped his twin brother’s heel as he was born (Gen. 25:26) “so his name was called Jacob.” It is also possible that Rebecca didn’t name her first-born son after Bethuel because this son was not the one who would rule after Isaac’s death.
Rebecca is central to Isaac’s claim as the heir to Abraham’s territory and to the divine promises, yet she doesn’t name her first-born son after her father, as was the common practice for sons who were to be rulers. This suggests that Isaac had another first-born son by another wife.
How do we track Isaac’s first-born by his other wife? We must look for the hidden third son, which involves looking for linguistic similarity as in the case of Og, Magog and Gog. When we do this, we find three sons of Abraham: Yitzak (Isaac) by Sarah; Yishmael (Ishmael) by Hagar, and Yishbak (Ishbak) by Keturah. We note the parallel names Yish and Yitz, which recall the 3-son confederations of the ancient Kushite rulers. 
Yishbak the elder would have had a grandson name Yishbak. This younger Yishbak is the first-born of Isaac by a daughter of Yishbak. She named their first-born son Yishbak after her father, according to the naming prerogative of the cousin bride.
Yishbak’s name means he will leave. He is likely one of the sons to whom Abraham gave gifts before sending them away to the east (Gen. 25:6). Yishbak’s descendants lived in the lands to the east of Canaan. Assyriologist Friedrich Delitzsch identified the name Ishbak with Iasbuk found on cuneiform inscriptions from a land whose king was allied with Sangara of Gargamis (Carchemish) against Assur-nazir-pal and Shalmaneser II (c. 859 B.C.). This Ishbak or Yisbak was likely a descendant of Abraham and Isaac.
It is fairly safe to conclude that Isaac had at least three sons and their names were: Jacob, Esau and Yishbak, the last being named by the cousin bride after her father, according to the cousin bride's naming prerogative. All three appear to have been rulers over their own territories.
Related reading: Moses' Two Wives
1. This pattern is like that of the Kushite rulers. The Kushite ruler Piye united Nubia and Egypt and established the 25th Dynasty. Before his death, Piye divided his kingdom between his 3 first-born sons, whose names are linguistically similar. Sheba-qo ruled in Thebes, Shebit-qo ruled in Napata, and Ta-har-qo ruled in Memphis. Shebaqo revived the office of high priest, which he awarded to his son Hori-makhet who was high priest in Thebes.