If you give your first child a family name, would you be concerned about giving your other children family names?

My parents gave me a family name (after my grandfathers first and middle). My brother has a family name but its a bit more distant (my moms uncle) but my sister is just a name they liked and my moms middle name. I think my sister sometimes feels like she got "less" of a family name because her first name is just something my parents liked.