The choice of whom to name a child after has always been made by the parents regardless of who died in what order. And it was not required that children be named after deceased grandparents. That was an honor given by the parents based on the regard they felt toward the deceased relative. And I should add that it was a joint decision.
When naming a child born in the US after someone who died, my maternal grandparents who were married in Russia chose American names closest to the Yiddish or Hebrew names of the deceased. However, as these first generation children grew up, they Americanized their names. For example, my mother's sister Bessie became Bernice. My paternal grandparents who were married here, Americanized their children's first names when they were born and gave them Hebrew names that were used for religious ceremonies. My father was named Bernard Howard after his grandfather Baruch Hirsh but went by the name Howard.
This naming convention of using the first letter of the deceased's name has continued and evolved further. Some people are named after more than one person using their first and middle names and others are named after someone using just their middle name.
