Why did Yaakov ask for the angel's name?
Seforno: In order to know its essence and what he had been sent for, so that he would be able to do Teshuvah and pray to Hashem. Ohr ha'Chayim - "Na" means now. [Most] angels do not have fixed names (rather, their names are based on their current mission).
Ha'amek Davar: Names of angels are based on their powers and actions for which they came to the world. It will be useful to know this when needed!
Why did the angel decline to give his name?
Rashi #1: Because angels do not have a fixed name, 1 but are called according to their mission. 2
Rashi #2 (in an original manuscript): Angels do not wish to give their names, in order not to take credit - seeing as they are merely servants doing the will of Hashem (and as such, they have no mind of their own).
Ramban: There was nothing to be gained in divulging his name, since, even if Yaakov were to call out to him for help, he would not answer him, nor would he save him in time of trouble. 3
Seforno: Angels are spirits whose existence is synonymous with their actions, which in turn, are determined by Hashem; they do not have a name per se. 4
R. Bechayei, Hadar Zekenim: It is normal for the victor to reveal his name, to be honored. The vanquished does not reveal his name, 5 lest he be shamed.
Meshech Chochmah (based on the Yerushalmi): One who blesses must know the name of the one whom he wants to bless. You need not know my name, for "Mevarachecha Baruch" - since I blessed you, automatically I am blessed.
Ohr ha'Chayim: I needed to know your name, to bless you. You have no need to know mine.
Malbim: The Yetzer ha'Ra is deficiency. It does not have its own essence. It changes from one form to another.
Ha'amek Davar: You pray to Hashem, the Power of all powers, so you do not need me!
Oznayim la'Torah: This is Nochrim's nature. They mock us, because when two Jews - who are total strangers - meet, they ask each other their names, where they are from and where they are going, and they exchange all their details, whereas Nochrim - like the angel of Esav, reply, 'what's it your business?!'
Rashi (to 32:25) explained that he was the angel of Esav. The Zohar and Midrash Tanchuma (8) say that his name is Sama'el! This was the angel's first time to sing Shirah (refer to 32:27:1:1). Perhaps he sensed that now his name will change, or he received his current name only after Yaakov defeated him! (PF)
Gur Aryeh: We know this is what the angel meant, for otherwise, why shouldn't Yaakov ask for his name?
Riva: The angel was concerned lest people put oaths on him if they know his name.
This is similar to Rashi's first answer (Refer to 32:30:2:1). See also Shoftim 13:18, where, under similar circumstances, the angel informed Mano'ach, that his name was Peli (hidden). Bamidbar Rabah (10:5) says that since he was sent for Nezirus, about which it says "Ish Ki Yafli..." (Bamidbar 6:2), he was called Peli.
Riva questions this, for it does not explain why the angel who spoke to Mano'ach did not give his name.
Why does the Torah write, "and he blessed him there"?
Rashi and Ramban; Gur Aryeh (to 32:27): Because the angel tried to avoid blessing Yaakov 1 immediately (refer to 32:27:3:1). But Yaakov refused to let him go until he blessed him there and then.
Malbim: The Yetzer ha'Ra does not have its own essence. It changes from one form to another. Its Berachah is according to what it is at the time.
Ha'amek Davar (also see Gur Aryeh to 32:27): When Yaakov let go of him, he thanked him and blessed him for this.
Asking him to wait until Hashem would bless him when he arrived in Beis El (See Hoshea 12:5).
Why did the angel decline to change his name there and then?
Oznayim la'Torah: Because he did not have permission from Hashem to do so.
Who blessed whom?
