Do we know what the name of Pharaoh (i.e. king or president) whom we were enslaved to when we were in Mitzrayim was?
According to this article by Mitchell First, if one accepts the chronology presented by I Kings (6:1), then combining that with other historical sources would lead to the conclusion that the Pharaoh of the exodus was Thutmose III. This assumes that the exodus took place in the 15th century.
If one is willing to suggest an error in I Kings, then First suggests that the Pharaos in question were likely Ramesses II and his successor Merneptah. This assumes that the exodus took place in the 13th century. Of course they were in Egypt for centuries, so during the course of the servitude multiple Pharaos would have ruled.
See First's article at length for a discussion of the merits and problems of the various theories.
According to this article, Prof. Yehuda Elitsur was of the opinion that the Exodus took place in the 15th century during the reign of Amenhotep II (the son of Thutmose III). (Interestingly, he identifies Moshe's adopted mother, Bitya, with Hatshepsut).
Interestingly, this (Christian) article, argues for Thutmose III. Based on Biblical and historical sources.
R. Aryeh Kaplan (The Living Torah, Ex. 1:8), suggests that it was Ahmose.
According to many modern professors and evidence found in Egypt and many other places (and based of different parts of Tanach) Dedumose II was the pharaoh of yetzias mitzraim.
According to them 2 Pharaos before him was the one that raised Moshe and the one before him was the whom torah said about him "ויקם מלך חדש" (it a machlokes rav and shmuel if its literal or not).