Can you refer me to a good source containing the genus and species name of different breeds of dogs?
All the different breeds of dogs - from Irish setters to greyhounds - are all part of the same species, canis lupus familiaris. The common, domesticated dog is actually a subspecies of the grey wolf. The different breeds do have different genetic characteristics (just as humans have, say, different eye or hair colors), but they're a all one and the same. The different names for different breeds are not like the scientific classifications of organisms via domain, kingdom, etc. They're just our choices.
All breeds of dogs are members of the same (sub) species: Canis lupus familiaris. "Breeds" of dogs are not scientific designations but are collections of traits recognized as unique by different breeding organizations. As such, certain breeds are recognized as unique in some organizations do not exist in others (see here for examples).