Contradiction with Exodus 3:6
Exodus 3:6, where God speaks to Moses from the burning bush, identifies Himself as the God of Abraham, Isaac, and Jacob, which seems to imply an existing relationship rather than introducing His name as if it were previously unknown.
Exodus 3:6: Moreover he said, I [am] the God of thy father, the God of Abraham, the God of Isaac, and the God of Jacob. And Moses hid his face; for he was afraid to look upon God.
Contradiction with Genesis 17:1
In Genesis 17:1, God introduces Himself to Abram as El Shaddai, meaning "God Almighty," suggesting that His identity was already known before the time of Moses.
Genesis 17:1: And when Abram was ninety years old and nine, the LORD appeared to Abram, and said unto him, I [am] the Almighty God; walk before me, and be thou perfect. [perfect: or, upright, or, sincere]
Contradiction with Psalm 90:2
Psalm 90:2 indicates God's eternal nature, suggesting that He has always been known as God, despite the claim in Exodus 6:2 of a new revelation of His name to Moses.
Psalm 90:2: Before the mountains were brought forth, or ever thou hadst formed the earth and the world, even from everlasting to everlasting, thou [art] God.
Paradox #1
Exodus 6:2 involves God speaking to Moses and introduces God's name as Yahweh. A possible contradiction is that earlier in Genesis, God was also referred to using the name Yahweh. This creates an inconsistency because Exodus 6:2 suggests that God had not revealed this name to the patriarchs like Abraham, Isaac, and Jacob, even though the text of Genesis uses that name.