My given name is Arthur Chase Brooks III, and my father was ACB Junior, and his father...anyway, you get the idea. I never heard of this being used for girl children. My grandfather's middle name was his mother's maiden name, which was a common naming convention in the US in the late 19th century. I expect that there are a lot more IIIs (and even IVs) around than you might think. It was very popular in my parent's day. so there were a lot of IIIs around when I was a kid. I dropped the III (unofficially) at the same time I began using Art rather than Arthur, and I think most other numerically designated people did as well (but I do allow anyone to put that name on a check if they want to....)