Benjamin Benyamin בנימין is composed of two parts - ben and jamin (yamin), meaning son of and right,, or literally, son of right (as opposed to left).
This is generally interpreted as meaning son of my right hand.
Since the root for right is identical to that for south, Benjamin alsas ho literally translated as son of the south; which refers to the birth of Benjamin in Canaan, as compared with the birth of all the other sons of Jacob in Aram.
In the Samaritan Pentateuch, the name is written as Benjamim בן ימים - with a terminal mem, literally translated as son of days; this may have been the original form, in reference to the old age of Jacob when Benjamin was born.
The name arose when Jacob deliberately corrupted the name Benoni, the original name.
Benoni, which means means son of my pain, was an allusion to Rachel dying just after she had given birth.