.. No. Israel was Prophet Jacob's nickname:

Genesis 32:28

And He said, “Your name shall no longer be Jacob, but Israel; for you have struggled with God and with men and have prevailed.”

Genesis 35:10

God said to him, “Your name is Jacob, but you will no longer be called Jacob; your name will be Israel.” So he named him Israel.

..etc, etc.

.. No. Israel was Prophet Jacob's nickname:

Genesis 32:28

And He said, “Your name shall no longer be Jacob, but Israel; for you have struggled with God and with men and have prevailed.”