Question: Why does David use his real name at the end instead of Walter's to gain access to the colonists and embryos? Wouldn't that been noticed in the log or something? He is pretending to be Walter in the first place and with the last log entry he uses the name Walter.
Answer: It doesn't matter anymore at that point. He has full control of the ship and can change anything he wants. Including the logs, if it's necessary.
Question: During the movie we learned that David felt some passion for Elizabeth for being kind to him before. So why use her body for his experiments after her death? Surely not to learn about human anatomy, which should be known to him already.
Answer: Regardless of his android passions, David was already experimenting with the bio-goo, and he deliberately used it to impregnate Dr. Elizabeth Shaw with a proto-face-hugger in "Prometheus." In "Covenant," we learn that David later killed Shaw and is experimenting with her body because her body tissues contain human-alien antibodies that are essential to David's work (which is creating a new generation of xenomorphs).
Chosen answer: If there had been a Queen, David would not have just left it there on the planet, he would have taken a Royal Facehugger embryo with him on Covenant. So the latter is most likely correct.