What exactly does Ben-Oni mean?
Rashi, Targum Onkelos and Targum Yonasan: It means 'the son of my pain.' 1
Rashi (to Bamidbar 26:13,24): It means 'the son of my mourning.' This was fulfilled partially after Aharon died and (and Bnei Yisrael wanted to return to Egypt, and Levi fought them, and) five families (from the 10 sons of Binyamin) were wiped out. It was fulfilled totally after Pilegesh b'Giv'ah (only 600 men from Binyamin remained).
Moshav Zekenim, citing R. Yeshayah: It is a Nefel (stillborn). Since she was about to die, she thought that he is a Nefel.
Malbim, Ha'amek Davar: It is my strength. I gave my strength to him; I died through him.
As in Devarim 26:14.
Why did Yaakov call him 'Binyamin'?
Rashi #1: Because he was the only one of his sons to be born in Eretz Kena'an, which is south of Aram Naharayim, 1 and Binyamin is the acronym of Ben Yamin (son of the south). 2
Rashi #2 and Rashbam: It means 'the son of my days,' 3 since he was born to Yaakov in his old age.
Ramban: 'The son of my strength. 4 Malbim - this is like Rachel intended!
'Rashi' on Bereishis Rabah 82:9, citing Rabeinu Sa'adya Gaon 5 : The son of anger.
Moshav Zekenim #1: When Yaakov was old, 6 he leaned on Binyamin.
Moshav Zekenim #2: This means a viable son, who will live many days.
Rashi: And Yamin means south, as in Tehilim 89:13. See Ramban (to 35:16,18), who cites a number of proofs that Aram Naharayim was (not north, but) east of Eretz Kena'an. He concedes however, that, assuming that Rachel died in the vicinity of Efrat (which is in the portion of Yehudah), then he was born in the south of Eretz Kena'an, though not if she died in the area of Har Efrayim, or even if she died in Binyamin's territory, both of which are described as being in the north. Refer to 35:16:2:1*. Harchev Davar (32:3) brings many supports for Rashi.
Rashi: This in turn, explains why "Yamin" is written Malei (with a 'Yud' before the 'Nun.' In most places, it is written Chaser, without the 'Yud'). Ha'amek Davar - The south is conducive to Chochmah.
Rashbam: And we find 'Yamim' written with a 'Nun' in Daniel 12:13.
Ramban: We find that Oni refers to strength (See Bereishis 49:3). The right-hand (Yamin) generally has strength and success. And he called him by that name to maintain the name "Ben-Oni" that Rachel gave him , but changed it to the good.
See Rashi to Tehilim 80:18.
I.e. he gave the name in his old age. Alternatively, he saw so through Ru'ach ha'Kodesh, and immediately gave this name (PF). Rosh - Yaakov immediately called him so, i.e. a son who will hold my right hand (support me) in my old age. (My other sons will be married.)
Why was Binyamin given two names, and what is their meaning?
Maharal (Chidushei Agados Vol. 2, p. 73, to Sotah 36a): The name given by Rachel, Ben Oni, indicates Din; while the name given by Yaakov, Binyamin, indicates Chesed. Binyamin was the completion of the twelve Tribes, and he therefore included all of their aspects - both Din and Chesed.
Of all the tribes, only Binyamin was born in Eretz Yisrael. How is this significant?
Maharal (Ohr Chadash to Esther 3:4, p. 129): All other lands have Heavenly officers appointed over them; only Eretz Yisrael is Hashem's portion. Binyamin, who was born in Eretz Yisrael, will have nothing to do with Avodah Zarah; that is why Mordechai did not bow to Haman.
Why does it say, "when her soul left, for she died"?
Moshav Zekenim: When Rachel wanted to die, they screamed at her. Her Neshamah was bewildered and returned to her, like we still do nowadays, and she called him Ben Oni.
Why did Yaakov change from the name that Rachel gave? It is a Mitzvah to fulfill the words of one who died!
Moshav Zekenim #1: When Yaakov was old, he leaned on Binyamin. 1
Moshav Zekenim #2: Her name was mistaken (she thought that he is a Nefel - refer to 35:18:1:3, 35:18:2:6, and 35:17:1.1:3). 2
Ramban, Malbim: The name's meaning remained the same. Refer to 35:18:2:3 and the note there.
How does this answer his question? Perhaps he called him Ben Oni until his old age; this fulfilled Rachel's words. His question is not clear to me. The Chiyuv to fulfill Divrei ha'Mes is only for property handed over to a third party (CM 252:2)! (PF)
The Nasi of Binyamin was named Avidan (Bamidbar 1:11) - Avi Dan means, 'my father judged correctly (that I am viable, unlike my mother thought)'.
