Went down this train of thought while participating in the sacred Passover ritual of watching Prince of Egypt, and thinking about how Moses's adoptive brother is named Ramses, as opposed to any of the other proposed Pharaohs. I do remember in sixth grade history class that it was mentioned that he was that Pharaoh—though I forget if it was taught as fact or hypothesis, nor do I remember if the implication was that the Exodus did in fact happen, or if this was presented as "If Exodus had happened, then he was the Pharaoh at the time." Of course, I am familiar with what the general consensus among historians is on the veracity of the Biblical story, so I suppose asking if any of those alternatives hold any water is a bit of a goose chase, but I am curious about the overall reasoning behind these theories and how compelling the cases are in pinpointing the real figure that aligns with the Biblical narrative.
Nevertheless, though, what's the reasoning for Ramses II to be the most popular name for Exodus Pharaoh, both in and out of academia?
The identification seems to owe principally to two things:
The mention of the "store-city" Raamses in Exodus 1:11. There were no Pharaohs called Ramesses until the thirteenth century, and Ramesses I had only a very brief reign (ca. 1295-1294 B.C.E.); Ramesses II (r. 1279-1213), on the other hand, oversaw the establishment of multiple sites bearing his name. Scholars who believe that Exodus tradition reflects some genuine history have generally associated the Raamses of Exodus 1:11 with Pi-Ramesses in the Eastern Nile Delta, one of Ramesses II's royal residences. Note that the other "store-city" in 1:11, Pithom, may refer to Per-Atum (at Tell el-Retaba?), another Ramesside site.
The mention of Israel in the late-thirteenth century Merneptah Stele. A monument set up by Pharaoh Merneptah (r. 1213-1204), Ramesses II's successor, contains our earliest reference to a people/place called Israel, although Merneptah claims to have destroyed them in the course of his campaign against Canaan. As the traditional thinking goes, if Israel existed at the time of Merneptah, then the Hebrews must have left Egypt sometime prior---but this assumes the historicity of the Exodus tradition, of course.
Richard Elliott Friedman's recent book The Exodus (New York: HarperOne, 2017) summarizes the scholarship in a very accessible way, if you're interested in reading further. He also makes a case (fairly convincing, in my opinion) for a historical Exodus that was originally much smaller, involving only the Levites, with the details become more and more elaborate over the centuries.
Sources and further reading:
Bietak, Manfred. "On the Historicity of the Exodus: What Egyptology Today Can Contribute to Assessing the Biblical Account of the Sojourn in Egypt." In Israel's Exodus in Transdisciplinary Perspective: Text, Archaeology, Culture, and Geoscience, ed. Thomas E. Levy et al., 17-37. Cham: Springer, 2015. (summarizes some relevant archaeological and geographical data, some of which concerns Pi-Ramesses and Per-Atum, and argues that the Exodus tradition preserves some genuine if muddled memories of enslavement in Egypt)
Currid, John D. Ancient Egypt and the Old Testament. Grand Rapids: Baker Books, 1997. (see pp. 126-129 for some discussion of Raamses and Pithom)
Hoffmeier, James K. Israel in Egypt: The Evidence for the Authenticity of the Exodus Tradition. Oxford: Oxford University Press, 1996. (a defense of the historicity of the Exodus by an Egyptologist with a conservative Christian background)
Kitchen, K. A. Pharaoh Triumphant: The Life and Times of Ramesses II. Warminster: Aris & Phillips, 1982. (an accessible overview of thirteenth-century Egypt; Kitchen's an accomplished Egyptologist who also has a conservative Christian background)
Propp, William H. C. Exodus 19-40: A New Translation with Introduction and Commentary. Anchor Bible. New York: Doubleday, 2006. (see Appendix B, "The Historicity of the Exodus from Egypt," 735-756, viewing the Exodus tradition as essentially myth)
Side question: How true was it that the Israelite population in Egypt as mentioned in the Bible were actually the Hyksos? And is it true that one of the Hyksos leaders' names was Moses, and that he led them when they were kicked out of Egypt?