Genesis 35:10 KJV
And God said unto him, Thy name is Jacob: thy name shall not be called any more Jacob, but Israel shall be thy name: and he called his name Israel.
Just as God had done for Abraham, God changed Jacob's name to Israel. It did not happen suddenly and it is not a part of his first relationship with God (as in when we get saved) this is something that happened years into his walk with God. I am reminded that a person's spiritual growth should not end early in their faith but there should be changes, even significant ones late into our walk with the Lord. We should never become stagnant with Christ. Even years after becoming a Christian there can and in many cases ought to be such changes in character that people (and more importantly, God) never see you the same. You become a new person with a new testimony and new reputation among your peers.
God grant that it is so.