Franklin: Practically everyone besides the title turtle. His friends include a bear named Bear, a rabbit named Rabbit, a beaver named Beaver, a fox named Fox, a snail named Snail etc. Apparently only turtles are creative enough to give their offspring names not taken after their respective species.
The main character in the short-lived cartoon series Family Dog did not have a name.
George of the Jungle: When he gets in a scrape, he makes his escape with the help of his friend, an ape named Ape.
Julius Jr.: Worry Bear sticks out like a sore thumb as the other characters have fantastic names like Julius and Sheree.
Bunnie Rabbot is a Funny Animal rabbit. Justified in that "Bunnie" is an actual name.
There is also Cat, the cat, and Lupe, the Wolf.
Sonic's non-humanoid dog is named Muttski.
South Park: Cartman's cat is called Mr. Kitty. Ironically, Mr. Kitty is female.
Parodied with the holiday episode, "Woodland Critter Christmas", where this trope is combined with Buffy Speak. The critters (who also happen to be devil worshippers) are named as follows: Squirrely the squirrel, Rabbity the rabbit, Beavery the beaver, Beary the bear, Porcupiney the porcupine, Skunky the skunk, Foxy the fox, Deery the deer, Woodpeckery the woodpecker, Mousey the mouse, Racoony the raccoon, and Chickadee-y the chickadee. It makes sense considering the entire story was cooked up by Cartman at the end of the episode.
Subverted in Tom and Jerry; Tom's name is actually short for Thomas, and is not just a reflection on the fact that he is, in fact, a tomcat.
Every character in WordWorld. Which makes a certain amount of sense, since most objects in Word World are made of the letters that spell what it is.
Young Justice has the alien robot sphere named Sphere and the albino wolf named Wolf. Lampshaded when Conner (who named the above two) is introduced to a monkey named Monkey. He says that's a good name.
Terrytoons' Deputy Dawg had a character named Al E. Gator.
The series features a giant pink lion by the name of "Lion".
The Gems all look humanoid but it's been shown their physical forms are an illusion and they're literally just their gemstone. So we have a pearl named "Pearl", a ruby named "Ruby", etc., despite the fact that there are more than one of each type. (The only exceptions are the Diamonds, who add colors to their names.)
The canine foil of Foghorn Leghorn had been identified on model sheets as Barnyard Dawg.
Downplayed with The Wild Puffalumps, as their names are actually the name of the animals that they are based on.
In We Bare Bears, The main characters are Grizzly the grizzly bear and Panda the panda bear. Averted with Ice Bear the polar bear.
A Little Curious has several members of its cast with names like this. "Mop" is a mop, "Mr. String" is a piece of string, "Plush" is a plush dog, "Little Cup" is a small cup, "Pad" is a notepad, and "Pencil" is a no. 2 pencil.
In Wanda and the Alien, Alien's name actually is "Alien", as revealed in one episode where the pair visit Alien's family when Alien is sick.
In Julius Jr., there is Worry Bear, who's name is in clear contrast to the other characters' names.
In the special The Easter Bunny is Coming To Town Sunny and his friends decide to deliver eggs in the somber town of Town.
Bear is this Goldie & Bear, except that it's not quite played straight - Bear is actually his last name. His first name is actually Jack, but when he was little his parents also called him "Baby Bear" and "Bear" ended up sticking.