Looking for sources explaining why the second book of the Torah is called Shemos?
If the answer is because that is the name of the first Parsha in the Sefer, why indeed is the Parsha called Shemos?
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In his introduction to the book of Exodus, the Netziv relates alternative names which the book is known by. For example, he notes that the appellation ‘shemos’ is indeed employed in midrashic sources, such as Bereishis Rabbah 3.
He likewise notes the Ramban’s title, ‘geulah’. He then continues to cite Bahag’s listing of the five books of the Torah as follows: Sefer Bereishis; Chumash Sheini; Sefer Kohanim; Chumash Hapikudim; Mishneh Torah. While the other four titles may seem familiar, the title ‘second’ given to the book of Exodus seems rather curious. For he should have either addressed them all in a numerical fashion, or named the book of Exodus based on one of its major events such as the exiting of Egypt or the giving of the Torah.
Therefore, he explains, it is specifically titled book two because it is the second part of book one. Thus, all of the purpose bound up in the creation discussed in book one is only realized completely after the events subside and come to fruition in this second part of the book.
[Based on this, it may be understood that the name shemos is equally important to reaching this end. Meaning, the purpose that is met in the climax of this book is only accomplished through the facilitators which bring about that goal. These are the ‘shemos’, names, with which the book begins.]
All Parshiyos and sefarim of Chumash are named after the first significant word in the Parasha. So since it begins ואלה שמות, that is its name. Parshas Toldos also gets its name from its beginning, "ואלה תולדות". This name is only used by convention, so although the name is very common in midrashim, nobody feels the need to justify it.
The Netziv in his commentary on Chumash does mention other names to the book of Exodus: The Book of Redemption, which is pretty self-explanatory, and the more puzzling title of The Second Book, which he explains at length. See there.
The Ramban writes:
The reason for "And these are the names" is that the verse wants to tell the topic of the exile from the time of their descent to Egypt because then was the initial exile, as I have explained. Therefore, it returns to the original topic which [originally was mentioned] in the verse, "And [Jacob] brought all his descendants with him to Egypt" (Genesis 46:7). Afterwards it says there, "And these are the names of the children of Israel who came to Egypt etc." This very verse is what is being repeated here, because even though they are two separate books (Genesis and Exodus), the story is connected with this one after that one....
So perhaps we name the whole of the second book of the Torah as Shemos-'names' because it is the next link on from Bereishis. We concluded that book by listing by name the exile down to Egypt and these people/names and their ensuing families would experience the שעיבוד מצרים, the slavery and bondage that followed.
And yet, despite this intensely bitter experience, the Jewish people remained true to who they were. A name is so much more than what a person is called. It represents a window into the soul.1 Indeed, we know the Midrash (Vayikrah Rabbah 32:5) relates that one of the things they maintained throughout their slavery was their names ("שֶׁלֹּא שִׁנּוּ אֶת שְׁמָם") i.e. they did not change their names or call their children by Egyptian names. They maintained their identity throughout. They became a tzibbur through their own enclave in Goshen and then became a people with the exodus and ensuing Mattan Torah.
As it writes here nicely:
In Hebrew the book is known as Sefer Shemot (“Book of Names”), because it opens with the verse, “These are the names of the children of Israel . . .” On a deeper level, this reflects the fact that it is the book in which our identity (name) as a nation is forged....The “Book of Names” begins with a nameless group of slaves, and ends with a G‑dly people, proudly bearing His name, honored to serve Him and make Him a home in this world.
1 The בעל שם טוב writes in פניני החסידות that the נשמה of a person is their central essence and when one looks at the אותיות הפנימיות, the central letters of the word "נשמה", you get "שם". Also refer to Gemara Brachos 7b that names can dictates one's future life.
So this is "And these are the names of the children of Yisrael who came to Mitzrayim: With Yaakob..." --
וזה ואלה שמות בני ישראל הבאים מצרימה את יעקב וכו' , שכשהתחיל לספר גלות מצרים וגאלתם התחיל משמות בני ישראל שבאים לשם, להורות שכל עקר קיומם בגלות וגאלתם משם, הכל היה בכח שמות בני ישראל שהם ראובן שמעון ולוי וכו', שכל שמותם נקראו על שם שמחת ישראל שעל ידי זה מבררין מהיכלי התמורות עד שמשיגין אור האין סוף וכו' שזה עקר תכלית הגאלה לדעת ולהכיר אותו יתברך כמו שכתוב וידעתם כי אני ה' המוציא אתכם וכו' . כי בשביל זה הקדים ה' יתברך שירדו יעקב ובניו הצדיקים בעצמן מצרימה, כי על ידי קדשתם העצומה שהיה מטה שלמה שהם גלו אלקותו בעולם שזהו עקר השמחה והחיות כנ"ל, על ידי זה היה להם כח לסבל מרירות הגלות ולבלי להשתקע שם.