We were discussing Sigmund Freud's "Moses and Monotheism" today, and this idea about Moses being Egyptian royalty was completely new to me. Apparently this idea was not unique to Freud, but what evidence is there to substantiate this? Freud's devotion to logic and scientific analysis are well documented, so I can't help but think there was some kind of, at least in Freud's mind, reliable source for this.
Well, for starters, the Moses character as portrayed in the Pentateuch is a mythical character, not a historical one. Furthermore, Freud's theory that Moses was Akhenaton or one of his followers is not widely held in biblical/historical scholarship.
That said, "Moses" is an Egyptian name. It has the same component mss that you get in other Egyptian names — Tutmoses ("begotten of Thoth"), Ramses ("begotten of Ra"), and so on. But it's missing the deity component that it most likely had at one time.
There have been a few serious proposals for a historical character that formed the kernel of the Moses tradition. One is prince Masesaya, who was briefly the pharaoh Amenmesse before being ousted c. 1200 BCE. Another is Ben-Ozen, a royal civil servant of Semitic origin who opposed forced labour of the Shasou in Timna and had the Egyptian name Ramses-em-per-Re. According to the ancient Egyptian historian Manetho, Moses was a priest of Osiris originally named Osarseph. There are some similarities between Manetho's story and Exodus, but these are probably due to literary borrowing (by the author of Exodus) rather than historicity.