Names are always a great place to start when studying the Bible. It could be the name of a person or a place but a quick look in your concordance will give you plenty of questions to start a Bible study off with.
One that I find interesting is when God changed the names of Abraham and Jacob. Abraham who started out Abram and Jacob who went to Israel have provided plenty of study time for me. It is this discrepancy of why when Abram went to Abraham he was never called Abram again in the Bible; Jacob on the other hand managed to be called both names through the rest of Scripture. Once Abram became the “father of many nations” that title stuck and the name change/prophecy went into effect.
Jacob or “heal catcher” became Israel or “he will rule (as) God” when he ran away with his family back to the land of Canaan. As you read that part of Genesis it would seem like God made the name change twice (chapter 32 & 35). But before you can get out of chapter 35 he is called Jacob again several times. In many places in Psalms and the Prophets the names Jacob and Israel appear together in the same passage.
Questions that are still waiting an answer: Did “Jacob” ever really become “Israel?” Did Jacob block, stop, or limit the change? Was this “limited” change on purpose; was the “perfect” will of God carried out?
Having asked those questions I will say this, it seems that the duel use of the names show a natural Jewish people and a spiritual Jewish people. And when I read many of the passages with both names it is very clear that both are equally loved and treasured.