Eddie Van Halen -- I Own a Tiny Dog ... and I'm DAMN Proud Of It!

Eddie van Halen says he's NOT ASHAMED by his fragile, cutesy-wootsy little pomeranian doggie ... despite his macho rock-god image ... telling TMZ he loves the little guy, no matter what other people think.

EVH was out in NYC last night ... cradling his poochie Kody on the way from his hotel to a waiting tour bus. The footage shocked some of the people in our newsroom who expected the rocker to own something a little less ...um ... Paris Hiltony.

But sources close to the dog tell TMZ ... Eddie has a strong bond with Kody ... and takes great care of his pet ... walking him, feeding and loving him every day.