Baal HaTurim on Shemot 1:1 of Parashat Shemot
1:1 Ve'eleh shemot benei Yisrael habaim - And these are the names of the Children of Yisrael who came.
The initial letters of these words spell shivya, captivity.  This indicates that even while the Jews were in [Egyptian] captivity, they [nevertheless maintained] the names of the Children of Yisrael, for they did not change their names.  As the Midrash (Pirkei DeRabbi Eliezer 48) teaches: Three merits allowed the Yisraelim to be redeemed from Egypt:
  1. They did not change their names - they retained their Hebrew names
  2. They did not change their language from the Holy Tongue to Egyptian
  3. They did not speak slander or gossip
Various Midrashim, e.g., Vayikra Rabbah 32:5; Shir HaShirim Rabbah 4:12 speak of four merits for which the Yisraelim deserved to be redeemed from Egypt, the fourth being that there was not a single instance of immorality.
Additionally, the conjunctive prefix vav of the word ve'eleh, "and" these are, indicates a connection between the subject of the previous narrative, And Yosef died... (Bereishit 50:26), and our verse, And these are the names..., namely, he [Yosef] commanded the Jews not to change their names.  Although the Egyptians changed his name to Tzafenat-paneach (Bereishit 41:45), he nevertheless told them, "You should not change your names." (Peirush HaRokeach).
Yisrael habaim - Yisrael who came.  The initial and final letters of these two words (when rearranged) for the word milah, circumcision.  And the final letters of et Yaakov ish, with Yaakov, each man, when read in reverse spell Shabbat.  This indicates that in the merit of the Shabbat and circumcision, which they observed while in Egypt, they were redeemed. 
Other Midrashim differ, however, and state that after Yosef's death the Yisraelim in Egypt either voluntarily abandoned the mitzvah of circumcision (Sifrei, Behaalotecha 67; Tanchuma, Behaalotecha 8), or were coerced by Pharaoh's decree to abandon it (Pirkei DeRabbi Eliezer 29).  Elsewhere, the Baal Turim's comments reflect these other Midrashim.
The verse begins with the letter vav (=6) and ends with the letter vav, alluding to the twelve tribes.  This phenomenon may be explained through a parable:
A builder  constructed a palace using only one pillar as a support, and it collapsed.  He rebulit it with two pillars and it caved in; with three pillars, and it crumbled. What did he do?  He built it with twelve pillars and it stood fast.
So, too, with regard to Avraham and Yitzchak, there was dross among their offspring, i.e., Yishmael and Esav, until Yaakov begot the twelve tribal progenitors among whom there was no dross. 
And so the Chosen People are called Benei Yisrael, not Benei Avraham, the Children of Avraham, because Yishmael is also Avraham's son, or Benei Yitzchak, because Esav is also Yitzchak's son (VeChur LaZahav).