Why was Yaakov's name changed from Yaakov to Yisrael?
Rashi: Because initially, he received the Berachos in a deceitful manner (b'Akavah), and now they were about to be granted to him openly (bi'Serarah). 1
Bereishis Rabah 78:3: Based on the Pasuk "va'Atzas Mal'achav Yashlim" (Yeshayah 44:26) - 'An angel told Yaakov that his name will be Yisrael, and I fulfilled his words!'
Seforno: The name 'Yaakov' shows that he will remain at the end of days, after the nations perish. Then, this name will not be needed, so he will be called 'Yisrael,' to commemorate the fact that he strove with an angel and with men and prevailed.
Even though the Pasuk seems to give a different reason - "because you strove before Hashem (Targum Onkelos) or with an angel (Targum Yonasan)... and prevailed." (EC)
Why did Yaakov's original name remain, even after he would be called Yisrael? (Also refer to 17:5:2.)
Maharal #1 (Netzach Yisrael, intro.): An effect remains along with its cause; and 'Yaakov' brings about 'Yisrael.' When the Jewish People humble themselves like an 'Akev,' (heel), then Hashem elevates them to the level of Yisrael - "you struggled with the G-dly, and with men, and overcame."
Maharal #2 (Tif'eres Yisrael, Ch. 37, p. 110): There are two aspects to the Jewish People's sanctity - a) They rise above physicality through Mitzvos; this is represented by the name Yaakov. b) They have intrinsic holiness through the Torah, represented by the name Yisrael. 1
Compare to 32:29:2.1:1.
Why did Hashem share His Name in our name, 'Yisrael'?
Maharal (Netzach Yisrael Ch. 10, p. 63): Yisrael is the Tzurah 1 (defining form) of the world. Were we to be lost among the nations, the world would be like a palace that lost its keys. Hashem attached His Name to theirs - like the chain by which the keys remained attached to the owner of the palace.
For more on the terms Tzurah and Chomer in Maharal, see 22:5:151:2*.
Why is the name Yisrael unique; seemingly the name Yishmael also contains Hashem's name (see Bereishis 16:11)?
Maharal (Netzach Yisrael Ch. 10, p. 63): Yishmael's name only tells us that Hashem heard his prayer [ - or Hagar's prayer - but does not indicate a Divine relationship with the nation descended from her]. The name Yisrael conveys the meaning of 'Serarah' - authority. This shows a G-dly aspect in the nation itself. 1
Ben Yehoyada (to Megilah 18): Additionally, unlike the name "Yisrael," the "Tzeirei" in Yishmael's name is under the Ayin, while the Alef is silent; thus, the name of Hashem is not fully pronounced.
What meaning does the name Yisrael convey?
Maharal #1 (Ohr Chadash, intro. (p.58)): The name Yisrael shows that we belong to Hashem. 1
Maharal #2 (Gevuros Hashem Ch. 67, p. 312): Adam was so named because he was created from the 'Adamah' (earth). 2 Yaakov, on the other hand, was holy, and disassociated from the material; and the name Yisrael means honor and authority.
Maharal #3 (Chidushei Agados Vol. 3, p. 176, to Sanhedrin 90b): The name Yisrael hints that the Jewish People are attached to Hashem, and are higher and above materialism; this is why "All of Yisrael has a share in the World-to-Come" (Sanhedrin ibid).
To whom are the terms "Elohim" and "Anashim" referring?
Rashi: 'Anashim' refers to Lavan and Esav.
Chulin 92a, according to Rashi, also see Maharal (Chidushei Agados Vol. 4, p. 110, to Chulin 91b): [Even though this is not the simple meaning in the Pasuk,] "Ki Sarisa" can be read as, 'you became an official (Sar).' It is hinting at two princes that would emerge from Yaakov - the head of the Galus, 1 who was wealthy and influential, and who therefore fell under heading of 'Anashim,' 2 and the Nasi of Eretz Yisrael, who had Semichah, corresponds to Elohim (judges). 3
Targum Onkelos: Elokim refers to [you fought in front of] Hashem.
Targum Yonasan: Elohim refers to the angel [with whom he had just struggled].
Chulin 92a, according to Harchev Davar (also see Maharal (Chidushei Agados, loc. cit.)): The order of the Derashos implies that Elohim alludes to the head of the Galus, who had more power, and 'Anashim,' alludes to the Nasi of Eretz Yisrael, who was really a higher level than the Reish Galusa.
Malbim: They refer to spirituality (Divine power) and physicality (human power. Refer to 32:29:151:2.)
Chulin 92a: Thus, the angel hinted to him that there will be exile.
Maharal (ibid.): According to Maharal, 'Elohim' means Mal'achim. Chutz la'Aretz is under the domain of the Mal'achim, as opposed to Eretz Yisrael; [therefore 'Elohim' would refer to the Babylonian exilarch - see 32:29:2:5.]
Maharal (ibid.): The two terms do not apply the verse to the king of Yehudah and the king of Yisrael, for in one land it would be better to have but one king.
In what merit was Yaakov able to overcome angels and men?
Maharal (Tif'eres Yisrael, Ch. 37, p. 110): We overcame men through of the sanctity of Mitzvos, represented by the name 'Yaakov.' We overcame angels by means of the sanctity of Torah, represented by the name 'Yisrael.' 1
Also refer to 32:29:1.1:2.
When was Yaakov's name actually changed?
Rashi (based on the Pasuk in Hoshea 12:5): When Yaakov would arrive in Beis El (35:9-10). However, the angel pleaded with Yaakov to let him go and sing Shirah 1 - promising Yaakov that he would be there as well and would lend his consent to the Berachos that Hashem would bless him there - a final seal of approval that the Berachos that Yitzchak had blessed him were rightfully his. Yaakov insisted that he bless him there and then, which he did. 2
How could the angel say "va'Tuchal," when Yaakov was limping, while he was not?
Oznayim la'Torah: Because the angel failed in his mission to topple the pillar of Torah from Yisrael.
What is the meaning of "Ki Sarisa Im Elohim v'Im Anashim, va'Tuchal"?
Ohr ha'Chayim: You overcame me; I could not leave without your permission.
Malbim: You are a composition of Divine power based on the Nefesh, which is a 'part' of Hashem, and human power, from physicality - Kol Yaakov and Yedei Esav. Yaakov wanted a Berachah for the end of days, when the Yetzer ha'Ra will be Batel and there is no more Avodah. You do not need this, for you overcame the physical - you are greater than [angels] that were never clothed in physical garments!
Normally, the bigger Chidush is taught last. Why does it say "Im Elohim v'Im Anashim"?
Ha'amek Davar: You were called Yaakov due to holding the heel. This hints to two matters. (a) When you are supreme, you will hold back Esav from asserting his kingship. (b) When you are low, you will want to hold Esav's heel and be under him, and not under others, who are less civilized. You do not need this name; when you are supreme, Esav cannot assert his kingship, for you overcame his Sar. When you are low, you need not be under Esav, for you prevailed against people, with Divine power. This is your Berachah! 1
Refer to 32:29:2:5.
It seems that the bigger Chidush is that he does not need the name, even for when he is low. (PF)
QUESTIONS ON RASHI
Rashi writes: "At the end, Hashem will appear to you in Beis El, and change your name...." Yet perhaps the verse means that Yaakov's name would change as of now?
Gur Aryeh #1 (to 32:27): The angel had no authority to change Yaakov's name; this was not his mission.
Gur Aryeh #2 (to 32:27): Rather than 'Lo Yikarei,' 1 the verse says 'Lo Ye'amer.' The Mal'ach merely informed Yaakov that Hashem would say this to him in the future.
See, for example, Bereishis 17:5.
Rashi writes: "Yaakov did not agree; and the Mal'ach was forced to concede over them [now]." How do we know this?
Gur Aryeh (to 32:27): The account concludes, "And he blessed him there" (32:30). Yaakov did not accept the Mal'ach's response (see 32:29:3:1); the latter was forced to bless (i.e. concede to) him immediately.
Rashi writes: "Yaakov did not agree; and the Mal'ach was forced to concede over them [now]." Why hadn't the Mal'ach wanted to bless Yaakov?
Gur Aryeh (to 32:27): The Mal'ach hoped to level additional accusations against Yaakov in the interim; perhaps Hashem would withhold His blessing, and the Mal'ach would not need to concede over Yitzchak's blessings.