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וְלֹא־יִקָּרֵ֥א ע֛וֹד אֶת־שִׁמְךָ֖ אַבְרָ֑ם וְהָיָ֤ה שִׁמְךָ֙ אַבְרָהָ֔ם כִּ֛י אַב־הֲמ֥וֹן גּוֹיִ֖ם נְתַתִּֽיךָ׃
And you shall no longer be called Abram, but your name shall be Abraham, for I make you the father of a multitude of nations.

First name change in Torah (Along with Sarah)

מה טובו אוהליך יעקב כו׳. להבין מארז״ל כל הקורא לאברהם אברם עובר בלאו שנאמר ולא יקרא עוד שמך אברם אלא מעתה הקורא ליעקב יעקב הכי נמי שאני התם דהדר אהדריה קרא כו׳. והענין שאי אפשר לבוא ולהגיע למדריגת ישראל כ״א בהקדימו תחלה מדת ומדריגת יעקב. ועיין בפ׳ וישלח דקע״ד ע״״א.

How goodly are your tents, O Jacob, etc." To understand from the words of our Sages: Anyone who calls Abraham "Abram" transgresses a prohibition, as it is said, "Your name shall no longer be called Abram." Instead, from now on, one who calls [him] Jacob, [the verse continues] "For that is your name," [indicating] that here too, since there is an enhancement, the verse enhances it, etc. The idea is that it is impossible to come and reach the level of Israel without first passing through the attribute and level of Jacob. See further in Parashat Vayishlach, paragraph 104, side A

Next is from this week's Parsha, Parshas Vayishlach

וַיִּוָּתֵ֥ר יַעֲקֹ֖ב לְבַדּ֑וֹ וַיֵּאָבֵ֥ק אִישׁ֙ עִמּ֔וֹ עַ֖ד עֲל֥וֹת הַשָּֽׁחַר׃

Jacob was left alone. And a figure wrestled with him until the break of dawn.

In Genesis Rabbah 77:3, the Rabbis teach that this 'figure' is Esau's guardian angel

וַיַּ֗רְא כִּ֣י לֹ֤א יָכֹל֙ ל֔וֹ וַיִּגַּ֖ע בְּכַף־יְרֵכ֑וֹ וַתֵּ֙קַע֙ כַּף־יֶ֣רֶךְ יַעֲקֹ֔ב בְּהֵאָֽבְק֖וֹ עִמּֽוֹ׃
When he saw that he had not prevailed against him, he wrenched Jacob’s hip at its socket, so that the socket of his hip was strained as he wrestled with him.
וַיֹּ֣אמֶר שַׁלְּחֵ֔נִי כִּ֥י עָלָ֖ה הַשָּׁ֑חַר וַיֹּ֙אמֶר֙ לֹ֣א אֲשַֽׁלֵּחֲךָ֔ כִּ֖י אִם־בֵּרַכְתָּֽנִי׃
Then he said, “Let me go, for dawn is breaking.” But he answered, “I will not let you go, unless you bless me.”
וַיֹּ֥אמֶר אֵלָ֖יו מַה־שְּׁמֶ֑ךָ וַיֹּ֖אמֶר יַעֲקֹֽב׃
Said the other, “What is your name?” He replied, “Jacob.”
וַיֹּ֗אמֶר לֹ֤א יַעֲקֹב֙ יֵאָמֵ֥ר עוֹד֙ שִׁמְךָ֔ כִּ֖י אִם־יִשְׂרָאֵ֑ל כִּֽי־שָׂרִ֧יתָ עִם־אֱלֹהִ֛ים וְעִם־אֲנָשִׁ֖ים וַתּוּכָֽל׃
Said he, “Your name shall no longer be Jacob, but Israel, for you have striven with beings divine and human, and have prevailed.”
ועם אנשים. עֵשָׂו וְלָבָן:
ועם אנשים AND WITH MEN —Esau and Laban.
לא יעקב [THY NAME SHALL] NO MORE BE CALLED JACOB [BUT ISRAEL] (literally, “not Jacob — supplanting — shall any more be said to thee”) — It shall no longer be said that the blessings came to you through supplanting and subtlety but through noble conduct (שררה) and in an open manner. Because later on the Holy One, blessed be He, will reveal Himself to you at Bethel and will change your name. There He will bless you, and I shall be there and admit your right to them (the blessings). It is to this that the passage refers (Hosea 12:5), “And he strove with an angel and prevailed; he wept and made supplication unto him” — it means the angel wept and made supplication unto him (Jacob). What was the subject of his supplication? This is stated in the next verse: “At Bethel He will meet us and there He will speak with us — implying the request. “Wait until he will speak with us there, and then I will admit your right to the blessings.” Jacob, however, would not agree to this, and against his own wish he had to admit his right to the blessings. That is what is meant when it states (v. 30) “And he declared him blessed there”, that he begged him to wait and he did not agree to do so (cp. Genesis Rabbah 78:2).

Genesis 32,26. “He said: ‘’let me go for dawn is ‎breaking’”. A look at Rashi on this line reveals that he ‎considers this a request by the spiritual alter-ego of Esau to take ‎his turn in the heavenly choir praising the Lord in the world of ‎the ‎שרפים‎, disembodied creatures, every morning. The Midrash, ‎‎(Bereshit Rabbah 78,2 and Chulin 91) commented that this ‎‎“angel’s” turn to recite these praises of the Lord had not ‎previously occurred so that he was most disturbed not to miss ‎this opportunity of doing so. We need to understand why this ‎angel’s turn to recite these praises of the Lord had come just ‎then.‎
It seems that the spiritual representatives in heaven of all the ‎nations sing the praises of the Lord. The timing of their doing so, ‎usually coincides with whenever one of the nations on earth ‎whom they represent in the celestial spheres, had performed an ‎act of kindness for the Jewish people. This enables their ‎respective representative at the heavenly court to act as a ‎powerful advocate on behalf of their charges down on earth. Esau ‎at that time had done a kindness for Yaakov, which enabled his ‎celestial representative to stake his claim to take his turn in the ‎lineup waiting to sing these praises in the heavenly choir. As this ‎had been the first time Esau had done something kind for Yaakov, ‎his spiritual representative had never yet had an opportunity to ‎be part of that choir.‎

The Lubavicher Rebbe, Likutei Sichot, Vol. 3, pp. 795-789 (summary)

Whereas the Torah no longer refers to Abraham as Abram once his name has been changed, the Torah continues to refer to Jacob as both Jacob and Israel. This is because the name Israel was not meant to replace Jacob's original name but to complement it, expressing a new, loftier status that he now attained. Whereas "Jacob" had to struggle with Esau and use trickery to secure Issac's blessings of material bounty, these blessings were now conceded to "Israel" openly by Esau's guardian angel.

Jacob's two names represent two ways in which we interact with the world. Sometimes the material world or our own materialistic tendencies challenge our Divine consciousness or mission in life; we must then, like Jacob, struggle to reveal the Divinity that underlies the materiality of the world.
At other times, the world can be used as a means to enhance Divine consciousness or fulfill our Divine mission; at such times our challenge, like "Israel," is to use these opportunities both to bring the world to a higher level of Divine consciousness and to promote our own spiritual growth.