I read that also, Barbie. You could have a family of four and all would have different last names!!
The Scottish and Yorkshire process is you name first son after your father. So if you were Joseph, and your father was William, your first son would be William and his first son would be Joseph. Problem comes when you have three sons you had named william, Robert, and John. Each would name their first sons Joseph, after you, and second boy after wife’s father. Ditto for women naming first daughter after her mother and you had multiple daughters.
So Eastons had a lot of Williams, Thomas, Joseph, and John in each generation!!! Women were mostly Jane, Sarah, Hannah, and Mary. Cousins seemed to all have same names because they had same grandparents. Plus, if they did not name kids after grandparents, they named them after siblings!!! Luckily people marrying into family brought a few names. They didn’t always follow these naming conventions but did it often enough to drive you crazy.