At this point, I don't have any great deal of useful Sotomayor commentary to offer, other than to link to Glenn Thrush's post mentioning that she has nephews named Connor and Corey, and a niece named Kiley. These are, to my knowledge, not traditional Hispanic names.
They are, however, vaguely Irish, or at least yuppified Irish, which is how immigrants display successful assimilation in this country. If you're going for the traditional Western names -- John, Richard, Jane, Mary -- you might be trying too hard, or maybe you just aren't familiar with enough Western names. Choosing a valorized Western non-Anglo-Saxon ethnicity shows that you've made it. (Of course, in my case it's the sort of assimilative device that retains still home-country flavor -- Neil is short for Neiladri, which means 'blue mountain.')