I meant the "John son of Jack" thing. It was extremely common for thousands of years across pretty much every European culture, and Jews (likely other people too but IDK). Eventually it transformed into surnames by Jackson. The important part is that surnames didn't introduce the idea of father's name being part of your name even if you're not named after him. This was already widely practiced, surnames just streamlined the process and made ancestry more trackable (though some countries still use the old rules to this day. Spain I think, and Iceland maybe?)

Dunno about other cultures, but in Poland it was very common until relatively recently to refer to wives/daughters by a suffixed first name (not surname) of the husband/father. If Mary Higgins married Jack Smith, from then on she'd be known as Jackowa, and their daughter Betty would be called Jackówna. This is distinct from naming children after their ancestors. The custom predates surnames by hundreds of years, but served essentially the same role of tying the women to their men.