Scriptural/theological reasoning for renaming: Abraham, Isaac, and Jacob I understand the significance of God's renaming.  But I wonder if anyone has done any research as to why the writers of scripture (and consequently, Jews and Christians today) refer to AbraHAM (changed name), Isaac (never offered a new name) and then JACOB (the name BEFORE God changed it to Israel)?  You never hear "Abram, Isaac, and Jacob" and you rarely hear "Abraham, Isaac, and Israel." (Though there are a few instances as pointed out below.)  Why is Jacob not granted his new name when his covenant participation is referenced?  Even in Genesis, once Abram is renamed Abraham in Gen 17:5, he is never again referred to as Abram, but "Jacob" and "Israel" continue to be used almost interchangeably throughout the Genesis narrative.  

Not simply looking for opinions, but rather if someone has had insight (possibly building upon the insight of others) that can shed light on this.  The theory has been posed that it could be as simple as avoiding confusion between Israel the nation and Israel the person - which is verifiable because it can be assumed that "Israel" was a people group even if Moses wrote the pentateuch with his own hand.   

If no significant research has been done on this topic, I may endeavor to spend a few weeks/months on answering my own question because I do believe it is valid and I do believe it is appropriately a matter of scholarly research.
In his monograph entitled The God of Abraham, Isaac, and Jacob, Dr. Richard D. Patterson observes that in the pivotal event in Israel's history when Elijah confronted the prophets of Baal on Mount Carmel, Elijah invoked the formulaic or motivic words you have drawn our attention to:


  “O Lord, God of Abraham, Isaac, and Israel, let it be known this day that you are God in Israel, that I am your servant, and that I have done all these things at your bidding. Answer me, O Lord, answer me, so that this people may know that you, O Lord, are God, and that you have turned their hearts back.”


Dr. Patterson then makes the following observations: 


  God sent a fire that not only consumed the sacrifice, but
  the altar itself and everything surrounding it. The use of the
  patriarchal formula not only reminded the Israelites of who was their
  God, but also demonstrated that those who are faithful to the Lord
  could call upon him and have their prayers answered (cf. Ps. 102:1-2.
  James 5:16-18). It is noteworthy as well that in the formula utilized
  here the patriarchal name Israel occurs rather than Jacob. For like
  Jacob of old, the Israelites of Elijah’s time (i.e., during the reign
  of Ahab and his wife Jezebel) needed to hold fast to the Lord if they
  were to experience his favor and blessing (my emphasis). 


In other words, if Dr. Patterson is correct, the Israelites as a nation, and at that point in their backslidden condition, needed to cling to the LORD just as Jacob did on the night the LORD appeared to him and wrestled with him. I suggest, therefore, that by implication Dr. Peterson is saying that Jacob as Jacob was a grasper of the heel of Esau (see Genesis 25:26), but Jacob as Israel was one who held on to God and would not let Him go until God blessed him. At that point, God changed his name from Jacob to Israel, meaning "one who has striven with God and man and prevailed" (Genesis 32:24-32). 

On Mount Carmel, then, Elijah is in effect telling Israel to keep holding on to God if you truly want to experience the LORD's blessing and prevail over the priests of Baal.

As for the other appearances of the formula, "Abraham, Isaac, and Israel," I'll leave them to another person who chooses to build upon my modest foundation of an answer!