2 Steps Forward, 1 Step Back
Once Jacob is renamed Israel, why does the narrator still frequently refer to him as Jacob?
I think it’s because, unlike with Abraham, who once he gets his new name keeps moving forward in the direction the Lord wants, with Jacob and his family, it’s always two steps forward and one step back.
For example, after the awful story of the rape of Dinah, Jacob does what he should have done before and moves the family to Bethel, commanding that they rid themselves of foreign idols. Good. But, then later we get the ugly news that Reuben, the eldest son (whose mother is Leah) sleeps with Bilhah, who is the mother of two of his other brothers and is one of his father’s wives/concubines.
This family is still not ready to be Israel, the people of God.
How they become so is the story told in part 3 of Genesis: Joseph in Egypt.