Basic Trope: Funny animal characters' last name is the name of that character's species.
Straight: "Say hello to Alice Cat and Bob Bunny"
"Now say hello to Tony Three Toed Sloth and Edgar Eastern Gray Kangaroo.
"I'd like to introduce you to Frank Felis Domesticus."
Downplayed: Funny animal characters have seemingly-normal last names which are related to their species, via Bilingual Bonus or a reference to prominent traits of the animal. Eva Garza is a heron, Jamie Fuchs is a fox, and Hannah Hopper is a frog.
Justified: When first assigning Surnames, it was customary to just pick a name that describes the family best, such as their species.
Invoked: The King of Animal Land, in an attempt to make record keeping easier, decrees that all family names should be the names of their species.
Exploited: Larry Lion wants a snack, so he checks out the phone book listings from Antelope to Zebra.
Defied: The various animals, tired of their uncreative names, all decide to change their last names to something cool.
Discussed: "The names in this town may not be very creative, but they're easy to remember."
Conversed: "How strange is it that all those characters have names related to their species? Can't the writers show a little more creativity?"
All animal characters have the last name as their species, meaning that all bunnies will have the last name of Bunny, whether their part of the same family or not. This makes meeting other animals of the same species very awkward, since nobody could tell whether their related to somebody of the same species or not, which made mating incredibly difficult. And dating outside of your species was frowned upon in this society either because it will mess up the naming system, or Hot Skitty-on-Wailord Action doesn't produce viable children in the setting, or both. This leads to several generations of inbreeding and confused identities. Eventually, it got hard to tell one member of a species from another, and all the animals eventually went mad.
Humans rule sapient animals like slaves, and deny them the right to have differentiated last names as a means to strip them of heritage and pride.
Animals now have a wider variety of names, much as in Downplayed. For example, a bunny could have the last name as Bunny, Rabbit, Floppy, Cottontail, Hopper, or several others. There are also more generic last names, such as Fuzzles, Scamper, Furball, Whiskers, among others.
After a successful revolt, having such a last name traces ones heritage to the revolutionaries, and is considered a great honor.