Like seriously, it sounds like a biker name, or maybe a Shaman name. I like it. I think it goes pretty awesome with your list.
I'd par it with a more conservative English middle name, since that seems to be the style you enjoy.
Hawkeye Thomas
Hawkeye Richard
Hawkeye Michael
Hawkeye Christopher
Hawkeye Joseph
Hawkeye Leo
Hawkeye Roger
Hawkeye James
Hawkeye George
Although now it's also starting to sound like a pirate name. Which is also pretty badass.