This name is a diminutive of … wait for it … David? (Weird.) It also may have been used in reference to people who lived in the southern part of Wales, by the river Taff. But its most common association these days is with the chewy, sticky confection we all love. And I don’t know about chewy, but your little Taffy will definitely be sticky sometimes.
Famous people named Taffy:
Journalist Taffy Brodesser-Akner; singer Taffy Nivert.
As a candy, taffy was first popularized in the United States during the 1800s.