"Cornbread" is young sparrow that hatched from an egg Sylvester was about to eat. It called the cat "Mama" for most of the episode, before switching to "Papa." Sylvester didn't have the heart to eat the bird and found himself protecting it from a series of unfortunate events.
The bird is never given a real name. "Cornbread" is just a derisive nickname that Sylvester calls him once.