As with most of these types of situational backstories, the answer is, well, situational.
Maybe they were adopted early on by another Roeg who isn't the birth father, but is treated in all respects as if the adopting family was their own, and takes on the name of the adoptive father (perhaps without their knowledge if it's at a young age).
Maybe they never found a family and had to live as a street urchin, and never really took a last name. Or, they use a surname that indicates the village/region they're from, for example with a -dyn appendix for -people instead of -syn or -wyn. Or to avoid coming up with a surname they just use their Eorzean-translated name instead of the original Roegadyn tongue.
I wrote this with the Sea Wolves in mind, but adapt the concept to any other clan and it's the same idea.