The Ramban says that Sefer Shemos is called Sefer HaGalus and also Sefer HaGeula since it is the story of both the Bnei Yisroel’s descent into Gauls Mitzrayim and their ultimate redemption. Not only is it the story of Galus and Geulas Mitzrayim but also encompasses the future Galus and Geulah.
Rav Elyashiv in Divrei Aggadah explains that Shemos is not simply the first significant word of this Sefer it is the actual reason for the Geula. The Medrash Yalkut Shimoni says that the name of each Shevet represents the future Galus. Two examples are Levi “V’Nilvu Goyim Rabim El Hashem” and Yosef “V’Haya BaYom HaHu Yosif Hashem Sheinis”.
This says Rav Elyashiv explains the significance of the fact that they did not change their names in Mitzrayim. They kept these names and guarded them carefully because they did not give up on the Geula. Their names gave them hope and showed their faith. Because of this faith which was expressed by the keeping of their original names they were eventually redeemed. That is why the Sefer of Galus and Geula is called Sefer “Shemos”.
Similarly the future Geula will come if we have faith and live our life waiting for that day.
