While the choosing of the English name is done more or less arbitrarily, the Hebrew name is normally given after the grandparents. (When more babies come, BH, they are named after the great-grandparents and so on). The source of this custom is literally pre-Abraham Abinu. The first recorded case of a man that named his son after his father was Terach, Abraham’s father. His father’s name was Nachor and he named one of his sons Nachor (Thanks to Mr Edward Dilamani for sharing with me this insight!).
In most Sephardic communities the first son or daughter is named after the father’s parents and the second son or daughter after the mother’s parents.
Parents should definitely keep away from asking mystical rabbis what Biblical names have “good luck or bad luck” or which “combination of names brings good luck or bad luck”. Those are mere superstitions and foreign practices that could bring unnecessary conflicts into the families. One example of a real case that happened in our community. A naive mother was told by a rabbi: Don’t name your newborn daughter “Rachel”, because Rachel (the Biblical Rachel imenu) died young”. Obviously, this absurd consideration does not make absolutely any sense. But the impressionable mother was now very scared for her daughter’s well-being and she refused to name her child after her own mother, Rachel, because of that ridiculous advice, causing a lot of pain to her mother.
Our Rabbis suggested in the case of Aharon and his sons, Nadab and Abihu, that actually when not naming one’s parents–especially when they have asked or wanted to be named–we should feel a great deal of consternation, for the consequences of depriving our parents from this high honor.
Click HERE to learn the differences between Sephardim and Ashkenazim when naming their babies after their parents.