Rashi says that the angel didn't change his name, only said that a name change would be coming. In trying to understand why he says that, I found an interesting, subtle difference in the text in the two passages.
Rashi on 32:29 says (emphasis mine):
no… Jacob: It shall no longer be said that the blessings came to you through trickery (עָקְבָה) and deceit, but with nobility and openness, and ultimately, the Holy One, blessed be He, will reveal Himself to you in Beth-el and change your name, and there He will bless you, and I will be there.“ He then acknowledged them (the blessings) as being his (Jacob’s). This is [the meaning of] what is written (Hos. 12:5): ”He strove with an angel and prevailed over him; he wept and supplicated him,“ [meaning that] the angel wept and supplicated him. With what did he supplicate him? ”In Beth-el he will find Him, and there He will speak with us“ (ibid). Wait for me until He speaks with us there. Jacob, however, did not consent, [to release the angel] and, against his (the angel’s) will, he (the angel) acknowledged them (the blessings) as being his (Jacob’s). This is [the meaning of] ”And he blessed him there," that he entreated him to wait, but he did not wish [to do so]. — [from Zohar, vol. 3, 45a]
Rashi is saying that the angel announced a future name change, but didn't actually effect that change. God made the change. (Siftei Chachamim and Rabbi David Zvi Hoffmann also understand it this way, h/t bjorne in comments.) It seems to me that this is consisent with past practice -- it was God, not a messenger, who changed Avram and Sarai's names to Avraham and Sarah, and here too, a patriarch's name change comes from God.
There is a subtle difference in the two texts. This is my own analysis, not Rashi's.
In Bereishit 32:29 the angel says the following:
וַיֹּאמֶר לֹא יַעֲקֹב יֵאָמֵר עוֹד שִׁמְךָ כִּי אִם יִשְׂרָאֵל כִּי שָׂרִיתָ עִם אֱלֹהִים וְעִם אֲנָשִׁים וַתּוּכָל:
And he said, "Your name shall no longer be called Jacob but Israel, because you have commanding power with [an angel of] God and with men, and you have prevailed."
The phrase יֵאָמֵר עוֹד שִׁמְךָ means, literally, "your name shall be said" (Yisrael). ("Called" is יִקָּרֵא and is used in chapter 35 below.)
Bereishit 35:10 says:
וַיֹּאמֶר לוֹ אֱלֹהִים שִׁמְךָ יַעֲקֹב לֹא יִקָּרֵא שִׁמְךָ עוֹד יַעֲקֹב כִּי אִם יִשְׂרָאֵל יִהְיֶה שְׁמֶךָ וַיִּקְרָא אֶת שְׁמוֹ יִשְׂרָאֵל:
God said to him, "Your name is Jacob. Your name shall no longer be called Jacob, but Israel shall be your name." And He named him Israel.
In chapter 32 the angel tells Yaakov that his name will be called Yisrael. In chapter 35 God actually makes the name change. In addition to the fact that the latter actually says "And He named him Israel" but the former doesn't, consider the differnece in the verbs. One is saying "your name will be called this" and the other is saying "your name will be this". The use of יִהְיֶה instead of יֵאָמֵר or יִקָּרֵא stands out in contrast to the other three uses: "your name is said" (Yaakov, 32), "your name will be said" (Yisrael, 32), "your name is called" (Yaakov, 35), and "your name will be" (Yisrael, 35).
I'm not aware of any other commentary based on these verb choices, but they stand out to me on a close reading.
As for why the text continues to call him Yaakov, that's a different question.
Please note: This answer was written for a neutral, academic audience
and is not intended to be interpreted in the context of a religious
belief or doctrine.