Genèse 35:18

And it was in the going forth of her soul, for death came upon her, that she called his name The son of my woe: but his father called him Benjamin.

‘BEN ONI’ (THE SON OF MY SORROW). I am of the opinion that he was so called because he alone was born in the land of Canaan which lies to the south (yamin) as one comes from Aram-naharaim, just as it is said: In the south, in the land of Canaan; Going on still toward the south. Binyamin thus means a son of the south, just as in the verse: The north ‘v’yamin’ (and the south) Thou hast created them. For this reason the name Binyamin is here written “full” [with a yud after the mem to indicate that the name is derived from the word yamin (south)]. This is Rashi’s language.
But I do not understand this claim that the Land of Israel lies to the south of Aram-naharaim for Aram is eastward of the Land of Israel, as it is written, And he came to the land of the children of the east, and it is further written, From Aram Balak bringeth me, the king of Moab from the mountains of the East, and Jacob crossed the Jordan which is to the east of the Land of Israel, and he returned by way of Edom which is south of the Land of Israel. Thus you find that Aram is south-east of the Land of Israel, and the Land of Israel is to its north. However, if Benjamin was born within the border of Bethlehem Ephrathah which is in the land of Judah — as it is written, Bethlehem in Judah, and it is further written, But thou, Bethlehem Ephratha, which art little to be among the thousands of Judah — this was in the south of the Land of Israel, and he was thus born between Beth-el and Bethlehem Ephrath. And if the place was in the hill country of Ephraim, then it is in the north of the Land of Israel, as it is written, Judah shall abide in his border on the south, and the house of Joseph shall abide in their border on the north. And if it was in the portion of Benjamin, it was also not in the south, for it is written, And their border was on the north side., Verse 12. Thus in any case there was no reason to call Benjamin “a son of the south.”
The correct interpretation appears to me to be that his mother called him ben oni, and she meant to say, “the son of my mourning,” similar in expression to: bread of ‘onim’ (mourners); I have not eaten thereof ‘b’oni’ (in my mourning). And his father understood the word oni in the sense of “my strength,” similar in expression to: the first-fruits of ‘oni’ (my strength); And to those who have no ‘onim’ (power). And therefore he called him Binyamin, “the son of power” or “the son of strength,” for in the right hand (yamin) there is strength and success, just as it is written: A wise man’s understanding is at his right hand; Thy right hand shall overtake all those that hate thee; The right hand of the Eternal is exalted., 118:16. Jacob wanted to call him by the name his mother had called him, for all his children were called by the names their mothers had called them, and he thus rendered it to good and to strength.
Now I have seen in Bereshith Rabbah: “Ben oni, ‘the son of my sorrow.’ And his father called him Benjamin, i.e., in the Sacred Language.” I do not know what this means for it is all the Sacred Language, and so are the names of all his sons in the Sacred Language. However, the Rabbis have alluded to that which I have said, namely, that Jacob rendered the expression so that it signified good.

BINYAMIN. Son of [my] old age [z'kunim]. Son of a long time [yamim]. As in (Dan. 12:13), "the end of days" [l'ketz hayamin], like "hayamim."

ויהי בצאת נפשה, while her soul was about to depart from her body,

כי מתה, ,for she was dying and there was no hope for her, she called him

בן אוני, for I gave birth to him in great pain;

ואביו קרא לו בנימין, meaning “the son of my right hand.” The name suggested that the child is especially beloved seeing that he was born when his father was already advanced in years. We find the word ימין used in the sense of being especially beloved in Psalms 80,18 וכן תהי ידך על איש ימינך, “grant Your help to the man at Your right hand, etc.” The end of the verse על בן אדם אמצת לך, “the one You have adopted as Your own,” spells out this meaning beyond any doubt.

בן אוני, “son of my sorrow;” she foresaw the tragedy involving the tribe of Benjamin in a civil war described in Judges chapters 19-21.