Nothing there indicates that God said He would be the God of Ishmael.
False; God sent his angel to name the boy after himself. Abraham prayed for Ishmael and God heard him. Although God would not use Ishmael as the father of Israel, God did bless him and deliver him. Abraham circumcised Ishmael. Read about it in Genesis. And Abraham said unto God, O that Ishmael might live before thee! And God said, Sarah thy wife shall bear thee a son indeed; and thou shalt call his name Isaac: and I will establish my covenant with him for an everlasting covenant, and with his seed after him. And as for Ishmael, I have heard thee: Behold, I have blessed him, and will make him fruitful, and will multiply him exceedingly; twelve princes shall he beget, and I will make him a great nation. But my covenant will I establish with Isaac, which Sarah shall bear unto thee at this set time in the next year. And he left off talking with him, and God went up from Abraham. And Abraham took Ishmael his son, and all that were born in his house, and all that were bought with his money, every male among the men of Abraham's house; and circumcised the flesh of their foreskin in the selfsame day, as God had said unto him. And Abraham was ninety years old and nine, when he was circumcised in the flesh of his foreskin. And Ishmael his son was thirteen years old, when he was circumcised in the flesh of his foreskin. In the selfsame day was Abraham circumcised, and Ishmael his son. And Sarah saw the son of Hagar the Egyptian, which she had born unto Abraham, mocking. Wherefore she said unto Abraham, Cast out this bondwoman and her son: for the son of this bondwoman shall not be heir with my son, even with Isaac. And the thing was very grievous in Abraham's sight because of his son. And God said unto Abraham, Let it not be grievous in thy sight because of the lad, and because of thy bondwoman; in all that Sarah hath said unto thee, hearken unto her voice; for in Isaac shall thy seed be called. And also of the son of the bondwoman will I make a nation, because he is thy seed. And Abraham rose up early in the morning, and took bread, and a bottle of water, and gave it unto Hagar, putting it on her shoulder, and the child, and sent her away: and she departed, and wandered in the wilderness of Beersheba. And the water was spent in the bottle, and she cast the child under one of the shrubs. And she went, and sat her down over against him a good way off, as it were a bow shot: for she said, Let me not see the death of the child. And she sat over against him, and lift up her voice, and wept. And God heard the voice of the lad; and the angel of God called to Hagar out of heaven, and said unto her, What aileth thee, Hagar? fear not; for God hath heard the voice of the lad where he is. Arise, lift up the lad, and hold him in thine hand; for I will make him a great nation. And God opened her eyes, and she saw a well of water; and she went, and filled the bottle with water, and gave the lad drink. And God was with the lad; and he grew, and dwelt in the wilderness, and became an archer.
Genesis, Catholic chapter seventeen, Protestant verses eighteen to twenty,
Genesis, Catholic chapter twenty one, Protestant verses nine to twenty six,
as authorized, but not authored, by King James