Remarkable is that no names are mentioned in Exodus 2:1–10, except Moses (see Exodus 2:10). It seems that the author wants to stress the facts, and not distract our attention with the names. God gives a new start to the people by keeping them anonymous.
In Exodus 6:1–30 we learn the names: Amram and Jochebed. We know the names from three children of them: Moses’ sister, Miriam, a prophetess (Exodus 15:20), and his brother Aaron, his companion when they went to Pharaoh and the later high priest.
1 Now a man from the house of Levi went and took as his wife a Levite woman.