The wrestler changes Jacob's name to "Israel," which means "one who wrestles with God"--which has profound implications for our relationship with Gof.
The OT prophets will now use "Jacob" and "Israel" interchangeably to designate God's chosen people.
Then Jacob reciprocates by asking the wrestler his name, a stupid question because (1) the wrestler has just told him He is God and (2) the wrestler has just given him a name that means "one who has wrestled with God."
So why does God refuse to offer His name? Because at that time, people thought that a divine name expresses the divine essence and God does not want to be put in a theological box in that way. Notice the OT pattern here. (1) When Samson's father, Manoah, asks "the angel of the Lord" His name, the angel indignnantly responds like Jacob's wrestling partner, "Why do you want to know my name (Judges 13:18)?" (2) When Moses asks God His name at the burning Bush, God is again characteristically evasive. Instead of offering a name, God substitutes a phrase "Tell them "I am whatever I am" or, better, "I will be whatever I will be" ... has sent you (Exodus 3:14)." Thus, God alerts Moses to the danger of an anthropomorphic understanding of His nature and instead wants to be known by His gracious acts of deliverance. God puts it this way to Isaiah:
"For my thoughts are not your thoughts, nor are my ways your ways, says the Lord. For as the heavens are higher than the earth. so are my ways higher than your ways and my thoughts than your thoughts (Isaiah 55:7-8)."
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