In Genesis 32, Jacob is returning to his homeland where he will see his brother Esau, whom he cheated out of his birthright and the elder son’s share of the inheritance many, many years before. He has a sleepless night, where he wrestles with a “man” who Jacob believes is God. Jacob demands a blessing and receives a new name – Israel.
The new name doesn’t seem to “take”. Jacob is still called Jacob after this, like in the Joseph story that begins shortly after this. And God is often identified as the God of Abraham, the God of Isaac, the God of Jacob.
The main place Israel is used is to identify the descendants as the nation of Israel. Among those who study ancient texts, this indicates a very strong likelihood that the stories of two different individuals have been merged into one. But this story does offer an explanation as to how the people came to be known as Israelites.