The most concrete character in these chapters is Moses himself. Setting him up as the protagonist for the rest of Torah, it is clear why his identity is consistent and certain. Although his identity is clear, his family’s is the most unclear in the chapter. His parents, along with his sister, are not named, even though they all play important roles in Moses’s survival and entrance into the hands of Pharaoh’s daughter.
As the main antagonist, Pharaoh’s identity is unclear throughout this, and the following story. The opinions range from one to three different Pharaohs that are conflated into one “Pharaoh.” He is framed as the main antagonist to Moses in the story, with some commentators saying that he is the same Pharaoh that was Joseph’s enemy as well.
Many of the other “secondary” characters in the story are left ambiguous as well. The handmaidens that save the children are not named, even though the Bible makes specific mention of them, their actions, and their reward.
Moses’s wilderness savior, Reuel, has an identity that is conflated with others as well. While many commentators say that he is Yitro, Rashbam argues and says that he is Yitro’s father.
The identities in the opening chapters of Exodus are unclear at many times. The stories take place over an extended period of time, with many of the characters changing. The Bible keeps them unclear to retain their roles throughout this and following stories. In order to properly set up this book, the main characters, Moses and Pharaoh, are identified, while the supporting characters are only identified to the extent needed as they move the plot along.