It’s definitely more unusual for a mother’s name to be passed along. That just follows our patriarchial society (not saying that as a political matter, just stating a fact.)
However, my mother was named after her mother, though they had different middle names.
Of course, you know that when a man names one of his sons after himself, the kid gets the full name, first, middle and last and a “Jr.” is attached.
He lives thereafter in his father’s shadow and strives to make his own identity. Not easy when you’re an “appendage” (strong word but I mean it) of your father, not your own individualist self.
I remember going to a minor league baseball game and there on one team was a player named Mickey Mantle, Jr. He tried and tried but he could not be the player that his father was; the team eventually dropped him off their roster. Despite—and maybe cause of—that name, he failed. Must be tough growing up under those circumstances.
If I had been given the name of my father I would have changed it at 18 or 21, whatever is the legal age requirement.
My wife and her mother share the same middle name. My wife hates it, because everyone knew her mom by that name.