Ben-Oni / Ben-Yamin The Naming and Re-Naming of Jacob's Youngest Child

(16) ...Rachel was in labor, and her labor was harsh. (17) When her labor was at its hardest, the midwife said to her, “Do not be afraid, for this one too is a boy for you.” (18) But as her soul was departing—for she was dying—she called his name Ben-Oni; but his father called him Benjamin. (19) Thus Rachel died. She was buried on the road to Ephrath—now Bethlehem.

Son of my suffering, for I gave birth to him in great pain

Son of my Mourning (Ben-Aveli).

Ben-Oni: There is in this two meanings: The language of suffering, as Rashi suggested; and the language of strength and vigor, for when he was born, he took her strength and her vigor, which she relinquished to him.

“Son of my sorrow;” Because of the incident of the pilegesh in Givah [which led to a civil war, described in Judges chapters 19-21], which would take place in the future under his name/tribe.

I am of opinion that he was so called because he alone was born in the land of Canaan which is in the South (yamin) as one comes from Aram-Naharaim ... Another explanation of בנימין is that it means “son of his old days (yamim)”

But his father called him Ben-Yamin, that is to say, "you are the son of my right hand, and you are especially beloved seeing that you were born in my old age." [Yamin is used here just as it is in Psalm 80:18] "So too grant Your help to the man at Your right hand" - the one who is beloved and precious to you, just as it says at the end of the verse: "and to the one You have adopted as Your own."

Ben-Oni means “son of my suffering.” Ben-Yamin: Rashi explains that this is because he along was born in the land of Canaan, which is in the south when one comes from Aram Naharayim, i.e. it is on the right hand side (yamin) of the traveler. Nachmanides objected, [and] instead explained instead that because his mother called him "Ben-Oni," which could imply "Son of My Mourning," ... his father simply translated it based on its good connotation, that is, the language of strength, like in [Genesis 49:3, the naming of Reuven] "the first of my vigor". Therefore, he called him Ben-Yamin, the son of strength, because the right hand (yamin) is the source of strength and salvation, for he wanted to call him essentially the same name that his mother gave him, for all children are called by the names that their mothers give them. It is only that Jacob translated his name using only its connotations of goodness and strength.

Ben-Oni - the language of suffering

But his father called him Ben-Yamin - He did not want to completely uproot from him the name of his mother; rather, he declared "Ben-Yamin," the language of strength.