It could also be possible you're mishearing the idiom "dog eat dog", which is a shortening of the phrase "it's a dog eat dog world". This means that it is a tough world in which anyone will do anything to get ahead.

It's nothing, except a name, "Snoop Doggy Dog" a doggy is an affectionate name for a dog, "hello little doggy!!". Doggy dog, it was a lovely little doggy dog. Snoop dog, was named after, "Snoopy" by his mother, Snoop doggy is an affectionate way to say Snoopy the dog. It's a bit like pussy cat, "pussy" doesn't mean anything to do with cats, there is a plant called pussy willow, a slang term for vagina is pussy, and if a wound is infected and has pus, it can be pussy (nice hehe not). Pussy cat, is an affectionate name for a cat, and probably comes from when people would say, "here pus, pus, pussy cat" trying to attract the cat so you could stroke it. How pussy ever got called pussy, I don't know, maybe because people want to stroke that too? Dunno, ask Americans. :) Doggy woggy, nothing to do with "wog" the racist term, (UK = black people, Australia = Italians). It just rhymes with dog - wog- doggy woggy. "Woggy" doesn't mean anything, unless you want to invent a word and say someone or some thing, is "wog like". (and go to jail if you get caught saying it online hehe)

basically an affectionate name for your dog. Though, I don't hear this as much as I hear "Kitty kitty".