Move over, chocolate lab: The labradoodle has arrived. Why walk a corgi when you can have a dorgi? Or coddle a poodle when you can cuddle a yorkipoo? Mutts, by any other name, are all the rage.

With a cute name and curly coat, doodle dogs seem to be incredibly popular with pet owners. They're favorites for people with allergies because they often promise little or no shedding. They are said ...