The Furious Five in Kung Fu Panda: Mantis, Tigress, Viper, Monkey and Crane. It's both a reference to their species and to the kung fu style they use. Though considering how Po is occasionally referred to as "Panda" it could be they're on a Last Name Basis, which invokes another trope altogether, but if so no one ever implies the Furious Five's given names.
The characters in the Toy Story movies are an interesting variation. Rather than being named for their species or occupation, most of them are named after the kind of toy they are. Thus, Mr. and Mrs. Potato Head are a Mr. and Mrs. Potato Head, Barbie and Ken are a Barbie and Ken, etc. Also applies to characters not based on real toys: Woody is a Woody doll and Buzz is a Buzz Lightyear action figure (one of hundreds, as we're shown). The straightest example of this trope would be Dolly the doll from Toy Story 3.