Why was Jacob's name changed to Israel?

Jacob was on the run from his brother Esau, after having stolen his birthright and blessing. After living in Laban's household for several years, Jacob was on his way back to be reunited with Esau. His journey back was filled with encounters with God.

As he was approaching Esau's land, Jacob sent his family ahead of him.

So Jacob was left alone, and a man wrestled with him till daybreak. When the man saw that he could not overpower him, he touched the socket of Jacob's hip so that his hip was wrenched as he wrestled with the man. Then the man said, "Let me go, for it is daybreak."
But Jacob replied, "I will not let you go unless you bless me."
The man asked him, "What is your name?"
"Jacob," he answered.

Then the man said, "Your name will no longer be Jacob, but Israel, because you have struggled with God and with men and have overcome."
- Genesis 32:24-30 NIV

This was a moment when Jacob's life was spared. He had an encounter with God and it changed his life -- and his name.