His name (Ishmael) was given by God through the angel, and stands as a perpetual reminder of God’s mercy. Ishmael means “God hears” — and understands, and will respond in times of need. It’s in the Bible, the Torah, Genesis 16:7-11, RSV. “The angel of the Lord found her by a spring of water in the wilderness the spring on the way to Shur. And he said, ‘Hagar, maid of Sarai, where have you come from and where are you going?’ She said, ‘I am fleeing from my mistress Sarai.’ The angel of the Lord said to her, ‘Return to your mistress, and submit to her.’ The angel of the Lord also said to her, ‘I will so greatly multiply your descendants that they cannot be numbered for multitude.’ And the angel of the Lord said to her, ‘Behold, you are with child, and shall bear a son; you shall call his name Ishmael; because the Lord has given heed to your affliction.’”
Again when Hagar and Ishmael were moving to Arabia the angel appeared to her. It’s in the Bible, the Torah, Genesis 21:17-21, RSV. “And God heard the voice of the lad; and the angel of God called to Hagar from heaven, and said to her, ‘What troubles you, Hagar? Fear not; for God has heard the voice of the lad where he is. Arise, lift up the lad, and hold him fast with your hand; for I will make him a great nation.’ Then God opened her eyes, and she saw a well of water; and she went, and filled the skin with water, and gave the lad a drink. And God was with the lad, and he grew up; he lived in the wilderness, and became an expert with the bow. He lived in the wilderness of Paran; [northern Arabia] and his mother took a wife for him from the land of Egypt.”