We say:" God of Abraham, Isaac, and Jacob..." God changed Avram name to Abraham and changed Jacob’s name to Israel. If we use the name change for Avram, why don’t we use the name change for Jacob?
There seems to be a difference in the nature of the renaming. In Avraham's case, the second name represents a progression or developement from the first. Originally Avraham was Avram, which means "father of Aram" - indicationg Avram's lofty status in his homeland. But after he left Aram Naharayim and went to Canaan, he was renamed Avraham, which the midrash interprets as "Av hamon goyim - father of many nations". It would not be correct to refer to Avraham by his old name that minimises his new status. In the case of Yaakov, the new name represents a totally different aspect of Yaakov's personality and spiritual life. Yaakov means bent or crooked. Yaakov's life experience constantly forced him into situations in which deveousnous was necessary, notwithstanding his natural aversion to such behavior. Yaakov also indicates the aspects of Yaakov;s life that have suffering and pain. Yisroel represents "yashar - straight" - the ability to accomplish spiritual (and non spiritual) tasks by confronting them directly (as in the meeting with Eisav). Both of these aspects of Yaakov's personality and experience are passed on to his children. Possibly we use Yaakov in prayer to represent that in prayer we are to humble ourselves and bend before HaShem's will/