Before Moses, there is possibly no other name more appropriate for God other than the God of Abraham, Isaac and Jacob. The reason is that God called Abraham out to populate a land given to a people that would serve him and then repeated the promise to Isaac and Jacob. The promise was to select a 'certain race', and how this particular line along that race race unusually ‘cut-out’ some of Abraham’s children, like Esau, takes a significant portion of the narrative on Genesis. The end result is an established 'exclusive racial descent’ from which a land was promised and from whose genes a Messiah would come to bless the entire world. In other words, there were two parallel promises being made. First a land for a people to live in, whom would serve God was promised to these fathers. In addition, a line of decent from which ‘all nations’ would eventually be blessed was sketched. Therefore, the whole notion of a select race, making God seem like a racists is actually a design to bless the world.
17 I will surely bless you and make your descendants as numerous as the stars in the sky and as the sand on the seashore. Your descendants will take possession of the cities of their enemies, 18 and through your offspring all nations on earth will be blessed, n because you have obeyed me.” (The New International Version. 2011 (Ge 22:17–18))
We see this promise of the land along this unique racial decent confirmed to all three patriarchs:
The land I gave to Abraham and Isaac I also give to you, and I will give this land to your descendants after you. (The New International Version. 2011 (Ge 35:12))
As the children of this promise eventually became slaves in Egypt they would have forgotten 'the God of the forefathers' to some degree. When Moses came as a prophet he naturally came in the name of the God who their fathers worshipped. He certainly could not approach them in the name of one of the gods of Egypt, or some other pagan country that had become overwhelmed with idolatry? In addition, Moses wanted a new name to describe 'the God' who had made a promise to their forefathers and God gave the name ‘I am that I am’ to the God of your forefather is actually I AM that I AM, the only God truly existent and eternal. In any case regardless of how we interpret I AM that I AM, the point is the I AM had previously made himself known to Abraham, Isaac and Jacob, choosing their line of descent to inherit the promise of land and a Messiah. Moses was now formalizing the rules and symbols of this covenant becoming a founder of all the laws associated with its policy. The racial selection was for the blessings of the world. The phrase ‘Abraham, Isaac and Jacob’ is therefore 'wonderfully racial' on that account. There is no other race from which the Messiah would come to bless us.
Abraham is especially relevant to the list of names because the promise was 'first' make to him. Jacob is also especially relevant in designating the race of Israel for he was the father of the twelve tribes, which for so long fully represented this people. Naturally Jacob is then the fitting ‘end point’ of the line of the patriarchal fathers. Conclusion: at the time of Moses when he approached the children of Abraham, the name ‘God of Abraham, Isaac and Jacob’ was possibly the most natural and fitting designation that reflects the relevant history of his salvation plan for the world through a racial separation.