That’s an interesting question because when a person’s name is changed in Scripture, it usually indicates that their character has been changed by some act of God’s grace. For example, Abram became Abraham, Saul became Paul, and so on. Yet, at the same time, there’s not an absolute discontinuity between their former name and their new name.
One of the things that makes this question even more complicated is that after God changed Jacob’s name to Israel, He still sometimes referred to Jacob as Jacob and Israel as the nation of Israel. Yet, at other times, He was referring to Israel, meaning the person Jacob, whose new name was Israel. If you try to work all those together, you better be prepared for an Excedrin headache because they can become very difficult.
Again, though, God revealed Himself first to Abraham, when he was Abram. Then, He revealed Himself to Jacob while he was still called Jacob. So, when God revealed Himself as the God of Abraham, Isaac, and Jacob, He’s talking about His history with His people. He is the one who revealed Himself to these three persons.
We could say the same thing in the New Testament, that He’s the God of Abraham, Isaac, Jacob, and Saul. Or, we could say He’s the God of Abraham, Isaac, Jacob, and Paul.