Jonathan Sacks points out that in Chronicles we are told that Pharoah's daughter was called Batya (The daughter of G-d). Just as she took Moses as a son, so too, in reward for her courage in adopting Moses, G-d takes her as his daughter.
He also answers my earlier question about Moses' name. In contrast to Joseph, who had an Egyptian name but was called Yosef in the Torah, Moses is only called by his Egyptian name. This is because theTorah wanted to give credit to Pharoah's daughter for having saved Moses.