When I mention I love Ryu, people tend to say "Eh, he's alright," and then I realize that they are referring to Ryu from Street Fighter or one of the other 5 billion Ryus. When I say "Hayabusa is a badass," everyone knows exactly who I'm talking about. Thus, I think "Hayabusa" is a much better identity for him and should remain his primary name of reference.
Only thing that confuses me is that I thought in Japanese you swap given and family names, so I figured it would be "Hayabusa Ryu." But, even in the Japanese versions, they always say: "Ryu Hayabusa." I'd love it if someone explained that to me,.