What animal are the Canary Islands named after?

Wrong, sorry. Anyone you just said canarys can go to the back of the class. The little yellow birds that Tweety Pie is based on are called Canarys because they come from the Canary Islands, not the other way around.
The archipelago actually gets its name from dogs.
The Romans, upon first discovering the islands called them the Isle of Dogs, so their modern name is derived from the old Latin Insula Canaria, after the large number of both wild and domesticated dogs they found there.
Dogs have been important in the Canary Islands in all known history, going right back to the ancient, Guanche, inhabitants. Archaeological excavations in several burial caves in Tenerife have shown that the dog was buried with his master, so it could "guide the soul to the region of the dead".
The importance of dogs to the islands continues right through to today, with dogs even being a main feature on the official coat of arms for the islands.

Happy Cruising