[Lukongsimi]

Good questions lah!  Jacob was named Israel when he wrestled with an angel of the LORD until daybreak lah! Saul/Paul wasn't mentioned yet until Acts 7 lah! Those who came out of Egypt were officially known as the Israelites lah!

Jacob Wrestles With God
22 That night Jacob got up and took his two wives, his two female servants and his eleven sons and crossed the ford of the Jabbok. 23 After he had sent them across the stream, he sent over all his possessions. 24 So Jacob was left alone, and a manwrestled with him till daybreak.25 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.26 Then the man said, “Let me go, for it is daybreak.”
But Jacob replied, “I will not let you go unless you bless me.”
27 The man asked him, “What is your name?”
“Jacob,” he answered.
28 Then the man said, “Your name will no longer be Jacob, but Israel,[a] because you have struggled with God and with humans and have overcome.”
29 Jacob said, “Please tell me your name.”
But he replied, “Why do you ask my name?” Then he blessed him there.
30 So Jacob called the place Peniel,[b] saying, “It is because I saw God face to face, and yet my life was spared.”
31 The sun rose above him as he passed Peniel,[c] and he was limping because of his hip.32 Therefore to this day the Israelites do not eat the tendon attached to the socket of the hip, because the socket of Jacob’s hip was touched near the tendon.. Genesis 32:22-32