ANSWER: You have asked a good question about the supposed battle between Jacob and an 'angel,' one to which not too many people know the answer. The answer is quite clear in the Bible but since too many Christians ignore the Old Testament other than for a few favorite 'tales' – David vs. Goliath, Adam and Eve, Cain and Abel, etc., not too many people have taken the time to understand the real truth contained in God's word.
The person who wrestled with an angel was Jacob, son of Isaac, grandson of Abraham. The story is that Jacob has traveled to the home of his mother’s brother, Laban to find a wife and wound up with two wives. Laban tricked him into marrying Laban’s oldest daughter, Leah, when he actually meant to marry her younger sister Rachel. He worked for Laban seven (7) years for each of the women and then decides to return to the home of his father Isaac. On the way back, Jacob sent his sons and wives across the ford (a shallow area where one could cross without too much difficulty) in the river Jabbok but he remained alone on the other side. Then, the Bible says, "and a Man wrestled with him until the breaking of day" (Genesis 32:24).
Jacob, completely by himself, wrestled with someone who he initially thought was just another man. When his opponent saw that he would not win, he touched Jacob's hip so that it wrenched it out of place. To this day the Israelites do not eat the tendon attached to the socket of the hip because of what happened. Although the man pleaded to be let go, he was not until he gave a blessing.
From the context and background of this story, we learn that the Hebrew name translated as Jacob means 'one who supplants.' He had stolen the birthright blessing from his older twin Esau, but Esau had already sold his physical birthright to him. Since God knew this was going to happen (Genesis 25:23) and He approved (Malachi 1:1-4 quoted by Paul in Romans 9:13), He got Jacob to tell Him his name during the wrestling match (verse 27) and then changed it to Israel (the Hebrew word which means 'to have power, as a prince'), thus removing the title 'one who supplants.'
As we read, the scripture does not say that this wrestling match was with an 'angel' but with a 'man.' Although the man does not give his name, Jacob understood that he had struggled with God and that he "saw God face to face" (Genesis 32:30). Because of this, many believe the person who fought him was actually God the Son - the same One who had appeared to both Abraham (Genesis 12:7; 17:1; 18:1) and Isaac (Genesis 26:1, 24) in the form of a 'man.'