It seems kind of cutesy sounding to me. Like more of a nn, or a pet's name, even. :-/ I've mostly familiar with it as a nn for
River (Calida here at BtN, and it was
River Phoenix's nn as well--IIRC, one of his sisters named her son
Rio after him). I'd have a bit of a hard time taking a man with the given name
Rio seriously, I think. And I'd also have the Duran Duran song in my head, too. ;)
Adding:
Liberty Phoenix has a son named
Rio Everest.