Canaries were named after dogs (sort of!)
It all has to do with the Canary Islands.
The wild canary is native to the Canary Islands, as well as the Azores, and Madeira. In the 17th Century, the first canaries bred in captivity were brought to Europe by Spanish sailors, becoming popular pets for the English and Spanish nobility.
The Canary Islands were named not after the yellow birds, but after dogs. In Latin, Canariae Insulae means Islands of the Dogs. Pliny the Elder claims that the islands contained “vast multitudes of dogs of very large size”, hence the names. The birds were named after the islands.
There is, however, one thing named after the birds: the colour canary yellow.
For another example of chicken-and-egg etymology check out: