When Jacob is renamed Israel, why is he still referred to as Jacob in subsequent passages? What, if any, is the difference between Jacob and Israel?
Shalom and thanks for the question!
YHWH changes the names of important people to suit his new role for them. Jacob means "supplanter" and YHWH changed his name to "Israel" which means "having power of God" (Genesis 32:28), because Jacob had "wrestled" with YHWH and won. So that's the difference between "Jacob" and "Israel." As we know, Jacob (Israel) went on to produce the twelve tribes of Israel (the nation).
Why is he still referred to as "Jacob" in subsequent passages? The name change did not mean that Jacob lost his given name and from then on would be called "Israel". It's unfortunate that the verse in English reads "Your name shall no longer be called Jacob, but Israel..." because the Hebrew word used is "shim'cha" is not necessarily "name", rather, it means "mark", or "honor/authority/character".
In other words, Jacob was given more of a title - "Israel". So in the following scriptures we typically see "Jacob" used when he is referred to as the man, Jacob, and as "Israel" when he is referred to has his new role.
This "renaming" is also seen in the New Testament. In John 1:42, Yeshua gives Shim'on a new "name" - Kefa - which means "rock". Later, we see him identified in Matthew 16:16 as "Shim`on Kefa" and Yeshua still refers to him as Shim'on (Matthew 16:17; 17:25; Mark 14:37; Luke 22:31; John 21:15-17). So, again, a "name" change is mostly a title due to some importance of that person, but it does not mean they no longer had their old name.