“And these are the names of the Children of Yisroel who came to Mitzrayim with Yaakov. Each person came along with his family.” (Shemos 1/1)
Zera Shimshon asks; the beginning of this possuk doesn't seem to match the end part of the possuk. In the beginning of the possuk Yaakov Avinu is referred to as Yisroel, the children of YISROEL, and then a few words later he is referred to as Yaakov, "...who came to Mitzrayim with YAAKOV." The possuk should have been written either, "And these are the names of the sons of Yaakov..." or "...who came with Yisroel to Mitzrayim. Why the change?
Zera Shimshon answers that in Parshas Vayigash (Beraishis 46/4) before Yaakov went down to Mitzrayim to see Yosef, it is written, "Vayomer Elokim l'Yisroel b'marras halailah vayomer, Yaakov Yaakov. Vayomer henayney"-And Hashem said to Yisroel in a vision at night; Yaakov, Yaakov. And he said back, "I am here. "Vayomer anochi Hakail Elokay avichah, al tirah mairdah Mitzraiymah key l'goy gadol aseemchah shawm." And He said; I am the G-d of your father. Don't be afraid to go down to Mitrayim because I will make you into a big nation there. "Anochi airad eemchah Mitzraiymah v'onochi a'alechah gam aloh v'Yosef yahshees yahdo al ainechah." I will go down with you to Mitzrayim and I will surely come up with you and Yosef will place his hands on your eyes.
There are two possible ways to understand Hashem's promise, "v'onochi a'alechah gam aloh" and I will surely bring you up. The first way is literal; Hashem simply promised Yaakov that he will not be buried in Mitzrayim but he will be brought up to Eretz Yisroel and buried there.
The second possibility is a looser interpretation; Hashem promised that there will be a redemption from Mitzrayim.
From the fact that the bondage of Mitzrayim didn't start until after the death of Yaakov, it is obvious that Yaakov was never in bondage in the first place, and therefore it cannot be that Hashem promised to take Yaakov out of bondage! It must be, then, the promise was only to take Yaakov out of Mitzrayim to be buried in Eretz Yisroel.
This is not true, though. Hashem promised to redeem Yaakov's descendants from Mitzrayim, and to show this, the Torah switches Yaakov Avinu's name from Yisroel to Yaakov in our possuk. How does this help?
Yisroel and Yaakov: Names and Meanings
The Zohar explains that even though both the name Yisroel and Yaakov refer to the same person, there is a difference between them. Yisroel is used when it refers to him when he lived comfortably in Eretz Yisroel. Yaakov is used when he is in distress.
This doesn't seem to be so simple, though. The above possuk relates that Hashem promised to Yaakov that he will be brought to Eretz Yisroel to be buried. This is prefaced by Hashem calling him, "Yaakov, Yaakov". Since Yaakov was still in Eretz Yisroel and not in bondage yet, why did Hashem call "Yaakov, Yaakov" and not "Yisroel, Yisroel"?
The answer is that since Yaakov was on his way to leave Eretz Yisroel, even though he was still living comfortably and not yet in bondage, he can be called Yaakov.
The Duality of Yaakov's State
According to the above, we can now understand why the Torah switched from Bnei Yisroel to "with Yaakov" and how this teaches that Hashem promised to redeem his descendants from Mitzrayim.
The possuk begins, “and these are the names of the Children of Yisroel who came to Mitzrayim” to show that even though Yaakov Avinu was not in his house he also was not in bondage, so, it is fitting to call him the prestigious name, Yisroel. However, to show that not being in his house is also a type of exile he is also referred to as Yaakov. In other words, when Yaakov went down to Mitzrayim he had in him an aspect of comfort and an aspect of distress.
From this that the Torah acknowledges that the going down to Mitzrayim itself even without bondage is also a level of distress we can also explain that the promise of "v'onochi a'alechah gam aloh" I will surely bring you" is referring to redemption and not only to the physical burial of Yaakov. Since Hashem promised to redeem Yaakov and not only that he will buried in Eretz Yisroel the redemption of his descendants is also included in this promise.
In short. We asked why in the beginning of the possuk, "V'aileh Shemos Bnei Yisroel" is Yaakov referred to by his name Yisroel and in the end of the possuk he is referred to as Yaakov. The answer is that it is to show that even before the bondage started Yaakov had some aspect of exile and distress in him. He was both in a state of comfort, connoted by the name Yisroel and a state of distress connoted by the name of Yaakov. This is important to know in order to understand that included in the promise of "v'onochi a'alechah gam aloh" I will surely bring you" is also the redemption of Bnei Yisroel.