The Second Book has had many names throughout history
In his introduction to the JPS Torah Commentary on Exodus, Nahum Sarna wrote the following (edited) regarding the name of the book :
"The commonly known Hebrew title...is Shemot.... This follows an ancient and widespread Near Eastern practice of naming a literary work by its initial word or words.
Another ancient Hebrew name was sefer yetsi'at mitsrayim...expressing its central theme. The Jews in Alexandria, Egypt...rendered this title in Greek as Exodos Aigyptou...which is how it appears in the Septuagint...the Vulgate and...in numerous European languages.... The Hellenistic Jewish philosopher Philo of Alexandria (d.50 CE) used this name and [wrote that he believed that] Moses himself had designated the title..... It was still current in Palestine in the 10th century.
Still a third Hebrew name for the book is mentioned in the Talmud [Sotah 36b]: Homesh sheni...."
(א) השלים הכתוב ספר בראשית שהוא ספר היצירה בחידוש העולם ויצירת כל נוצר ובמקרי האבות שהם כענין יצירה לזרעם מפני שכל מקריהם ציורי דברים לרמוז ולהודיע כל עתיד לבא להם.
ואחרי שהשלים היצירה התחיל ספר אחר בענין המעשה הבא מן הרמזים ההם. (ב) ונתייחד ספר ואלה שמות בענין הגלות הראשון הנגזר בפירוש ובגאולה ממנו. ולכן חזר והתחיל בשמות יורדי מצרים ומספרם אע"פ שכבר נכתב זה בעבור כי ירידתם שם הוא ראשית הגלות כי מאז הוחל.
והנה הגלות איננו נשלם עד יום שובם אל מקומם ואל מעלת אבותם ישובו. וכשיצאו ממצרים אע"פ שיצאו מבית עבדים עדיין יחשבו גולים כי היו בארץ לא להם נבוכים במדבר. וכשבאו אל הר סיני ועשו המשכן ושב הקב"ה והשרה שכינתו ביניהם, אז שבו אל מעלות אבותם שהיה סוד אלוה עלי אהליהם (see Job 29:4) "והם הם המרכבה" (Ber.Rabba 47:8) ואז נחשבו גאולים.
ולכן נשלם הספר הזה בהשלימו ענין המשכן ובהיות כבוד ה' מלא אותו תמיד.
Rabbeinu Moshes ben Nahman was born in Gerona in 1194. Rashba writes that Ramban was a physician. He composed commentaries on the Talmud, criticism of Rambam's Sefer HaMitzvot, responsa, commentary on the Torah and various biblical books, philosophical treatises, composed poems and piyutim, halakhic works, and was regarded as principal Rav of the Sefardi world and beyond. He developed a middle position during the Maimonidean controversy (started 1232) but it did not prevail. In 1263 he was forced to participate in a disputation with the apostate Pablo Christiani. King James I of Aragon deemed him to have defended his faith, but Pope Clement IV sought to penalize Nahmanides. He fled to Acre in 1267 and died in Israel. Over 50 of his surviving works remain primary sources on many aspects of Judaism. ..............................................................................................................................................
In the Book of Genesis, which is the book of Creation, the Torah completed the account of how the world was brought forth from nothingness and how everything was created, as well as an account of all the events which befell the patriarchs, who are a sort of creation to their seed. All the events that happened to them were symbolic occurrences, indicating and foretelling all that was destined to come upon their seed.
After having completed the account of creation, the Torah begins another book concerning the subject that had been alluded to in those symbolic events [recorded in the Book of Genesis]. (2) The Book of V’eileh Shemoth was set apart for the story of the first exile, which had been clearly decreed, and the redemption therefrom. This is why He reverted and began [this second book of the Torah] with the names of those persons who went down to Egypt, and mentioned their total number, although this had already been written. It is because their descent thereto constituted the beginning of the exile, which began from that moment on.
Now the exile was not completed until the day they returned to their place and were restored to the status of their fathers. When they left Egypt, even though they came forth from the house of bondage, they were still considered exiles because they were in a land that is not theirs,. entangled in the desert. When they came to Mount Sinai and made the Tabernacle, and the Holy One, blessed be He, caused His Divine Presence to dwell again amongst them, they returned to the status of their fathers when the ‘sod eloka’ (company of G-d) was upon their tents and “they were those who constituted the Chariot of the Holy One.” Then they were considered redeemed.
It was for this reason that this second book of the Torah is concluded with the consummation of the building of the Tabernacle, and the glory of the Eternal filling it always.
A Digest of Ramban's Introduction:
B'reishit dealt with the story of creation in three regards:
-creation of the world from nothing
-fashioning of its elements
-the events of the Fathers - the "fashioning" of the future generation, because
the events of the Avot foretold the future of the later generations. (Mystical idea)
After these stories of the various "creations," a new book began which contained the events hinted at (foretold) in the first book. Its distinguishing themes: Galut and Geula.
Galut was explicitly stated in Gen. 15: 13-16, at the Covenant between the pieces.
Given the connection between these books, common elements are repeated in both to link them together: the names and number of those exiled to Egypt, which was 70.
Galut is concluded when they return to their former location (Canaan) and to the (spiritual?) level which they occupied previously. Although they were brought out of Egypt, they were still in Galut since they were in a foreign land.
Geula: only after they reached Mt. Sinai and constructed the Mishkan, could the Shechina dwell in their midst. Thus, the conclusion of Sh'mot details the construction of the Mishkan so God's presence could dwell in it in perpetuity. The book details the nation's movement from Galut to Geula.
Rav Naftali Tzvi Yehuda Berlin (Netziv):
Born in Belarus in 1816, died in 1893. Opposed to the dominant "lomdus" method of the yeshivot, he favored examining sources historically, starting with Tannaitic material and using Geonic literature. He was Rosh Yeshiva of the famed Volozhin Yeshiva for almost 40 years. He wrote on Geonic literature, issued responsa, commentary on entire Tanakh, and various halakhic works. Highly regarded today as creative and unique scholar. After daily morning services he gave a shiur on Humash.
He was an early supporter of the Hovevei Zion movement and strongly supported the resettling of Eretz Yisrael. However, he was opposed to the selling of the Land for the Sh'mitah year. Contrary to the view of Rav Hirsch, he opposed setting up separate communities.
The Maskilim could not bear the success of the Yeshiva and constantly sought its demise. Their continuous barbs were noted by the government who demanded that the Yeshiva curriculum and hours of study be completely revamped. If the government’s demand were followed, the Yeshiva would have totally lost its character. It closed its doors.
After its closing, his health began to decline and he died less than two years afterwards. His two sons were Rabbi Chaim Berlin and Rabbi Meir Bar-Ilan.
(א) זה הספר נקרא בפי בעלי המדרש ספר שמוT.... וכן בהרבה מקומות.
The Ramban called it ספר הגאולה. זולת רבינו בה״ג...יקראהו ספר שני דקחשיב "חמשה חומשי תורה. ספר בראשית. וחומש שני. וספר כהנים. וחומש הפקודים. ומשנה תורה...." שלא בחנם שינה השם בזה הספר. והיה לרבינו לקרוא כולם במספר, חומש שני ושלישי וכו'. או חומש שמות. או על הענין המסוים שבו כמו יציאת מצרים או מתן תורה. כמו שקורא ספר במדבר. ספר הפקודים.... אלא בא ללמדנו דזה הספר ביחוד הוא שני לספר ראשית-הבריאה, כי הוא חלק שני מזה הספר. היינו בו נגמר סדר הבריאה. וכמאמרם..."בראשית- בשביל ישראל שנקראו ראשית. פי' תכלית העולם בכלל. הוא שיהא אומה אחת חלק ה׳ עמו. וזה לא נשלם עד שיצאו ישראל ממצרים ובאו לתכליתם שיהיו ראוים להיות לאור גוים להעמידם על ידיעת אלהי עולם.... וזהו תכלית הבריאה שנברא לכבודו ית׳.... נמצא דיציאת מצרים הי' גמר הבריאה או מ"ת....
והיינו כדאיתא בעבודת כוכבים ד״ג: ויהי ערב ויהי בקר יום הששי-מלמד שהתנה הקב״ה עם מעשה בראשית, אם מקבלין ישראל את התורה מוטב ואם לאו אני אחזיר אתכם לתוהו ובוהו. נמצא דמתן תורה הוא גמר הבריאה והיינו הך דיציאת מצרים שאז היו ראוים ישראל לקבל התורה ולהשלים הבריאה ולבא בזה לתכלית יצירתם. והרי זה אצל עם ה׳ כמו דעת אנושי ומדות ישרות של תורת האדם. אשר אע״ג שלא הגיע תבל ומלואה לזה השלמות עד אחר זמן רב אחר בריאת שו״א - וגם כהיום יש הרבה בני אדם שלא הגיעו לזה המעלה - מ״מ הדבר מושכל גם לאוה״ע, דרק זה הי׳ תכלית מעלת האדם. וכך יש לנו להאמין דאע״ג שלא ניתנה התורה וחקותיה עד אחר יציאת מצרים - וגם עתה יש הרבה מישראל שלא הגיעו לדעת תורה - מ״מ רק התורה היא תכלית מעלת ישראל. שנוצרו לברית עם לאור גוים.
נמצא דספר שמות הוא ספר שני להראשון כמו שהמה ענין אחד ובו שני חלקים של ספר הבריאה:
(1) This book is commonly referred to by the authors of the Midrash as Sefer Sh'mot, ... and similarly in many other locations. Nachmanides, at the end of his commentary calls it the Sefer HaGeulah . However, our Teacher the BaHaG...refers to it as the “Second Book....” [We likewise find Sh'mot referred to as the “Second Book” in Tractate Sotah 36b.] Our Rabbis should have [been consistent and had either] listed all five books according to their numeric order, i.e., the Second Book of the Torah, the Third Book, etc.; or [this book] should have been titled the "Book of Names," or any other name depicting its theme, i.e. “Exodus from Egypt” or the “Giving of the Torah,” just as the Book of Bamidbar is called Sefer HaPekudim.... In fact, it comes to teach how this book specifically is the second volume to the book describing the beginning of creation; i.e. it is a second section describing the culmination of creation. This is like our Sages of Blessed Memory stated, God created the world for the sake of Israel who are called reishis, “first,” as stated “[Israel is holy to the Lord] the first of His crop”; (5) The understanding of this is that the purpose of the world’s creation as a whole was for a single nation to become God’s possession, His nation. This did not completely come to fruition until Israel left Egypt, arriving at their purpose when – upon accepting the yoke of the Torah and mitzvos – they experienced a transformation of their very being....
This is also stated in Tractate Avodah Zarah 3a: (8) What is conveyed by the phrase, “And there was evening and there was morning the sixth day?” It teaches us that God made a condition with the works of creation, saying: “If Israel accepts my Law it will be well, but if not, I shall reduce you [the world] to a state of chaos and void.” Thus the giving of the Torah completed creation. It is the same as the exodus from Egypt for only [through the exodus] could Israel be capable of receiving the Torah, thus actualizing the purpose of their conception.
The wisdom of the Torah possessed by the Lord’s Nation is similar to human morals and proper character traits (i.e., ethics). For even though the entire world did not achieve this goal until after a great amount of time following the creation of heaven and earth - and similarly even today there are many who have not achieved [the proper] level [of ethics] - nevertheless, it is well-understood even by the nations of the world that this is the purpose of man’s stature. Similarly, we, the Nation of Israel, need to believe that even though the Torah and its statutes were not given until after the exodus from Egypt and, even currently, many Jews have not reached [the level of incorporating] Da'at Torah ; nevertheless, it is only the Torah that is the ultimate purpose of Israel’s stature. [We] are created for this [purpose], and it is the reason we have been ‘placed [on this earth] for a covenant of the people, to be a light of the nations.’
It then follows, why the Book of Sh'mot is considered as a second volume to the first book, as both books deal with the same theme; they are the two parts that describe the creation.