Barney Gumble is Homer Simpson's best friend while Barney Rubble is Fred Flintstone's.
Oddly enough, the Transformers franchise does this within itself. Being named Prowl, Thrust, Snarl, Inferno, or one of any of the other most common names in the Cybertronian phone book, it doesn't mean you've got anything in common with anyone else with the same name.
The toyline, however, is another story. As is the way of these things, fans are a lot more concerned with continuity and such than the makers who just want you to buy it, so when two dissimilar toys are given the same name in the same toyline, or a toy with the name of a character it doesn't resemble comes out, the Epileptic Trees get planted as people try to figure out when the scant lines of bio "take place." Prowl the owl and Prowl the lion both released as Beast Wars toys? Are they the same guy? Which one, if either, is the same guy as G1 Prowl? There are, in fact, a ton of toys named Prowl that don't exactly mimic any character named Prowl and are hard to place. Transformers Wiki has a page for each of them, and even some of those pages have a "this is what we think we know; even we can't be sure" section.
One weird case is Sky High, which was used for a Pretender one year and then a Micromaster the next, with no relation between the toys.
In-fiction, there's the Unicron Trilogy, where some Transformers Armada Mini-cons have their names re-used for full-sized characters. Most of them don't get their names spoken onscreen, but a few do: The names Dirt Boss, Downshift, Mirage, and Blackout, we'll be hearing from again with characters who clearly cannot be the same ones. Also, the Mini-con helicopter Jolt may or may not be a case: despite both being Mini-con helicopters named Jolt, it's hard to reconcile the backstories of the Armada and Cybertron versions. Also, some Beast Wars characters share the names of unrelated Generation 1 characters (while some, like Starscream and Ravage, are the G1 characters. The show is quite clear on who's who.)
The movieverse has another version: non-movie material such as comics often movie-ify past characters and use them, and the next movie comes out and uses the same name with an unrelated character. Sometimes Arc Welding is used (we find out how Arcee becomes one 'bot with three bodies), sometimes not (there's no slagging way Movie 1 Comic Mudflap and Revenge of the Fallen bad racial stereotype Mudflap are the same guy.)
Japan's got a different version: Most versions of Optimus Prime are called Convoy. Some get a prefix (Fire Convoy, Grand Convoy, etc.) but then, so do leaders who are not based on Optimus himself (as the rank Prime is also called Convoy.) Furthermore, what America considers a reboot and what Japan considers a reboot aren't always the same. Therefore, if a character looks like Optimus Prime and is called Convoy or Something Convoy it is impossible to know if he is intended to be (a) the same character as; (b) a rebooted show's version of; or (c) a completely different character who happens to be similar to any other given Convoy or Something Convoy.
Real Life instances were lampshaded in Histeria! by a Running Gag where Squeeing fangirl Pepper Mills would hound a historical figure for an autograph, only to be disappointed that she'd gotten the wrong person. For instance, she mistook Leonardo Da Vinci and Vladimir Lenin (in separate skits) for Leonardo DiCaprio and John Lennon.
Dinky Dalton (Huckleberry Hound, Laff-a-Lympics) and Dinky Dog (The All-New Popeye Hour)
Two Ant Hill Mobs: A gang of insect bikers in the Atom Ant cartoon "Bully for Atom Ant", and the mobsters from Wacky Races and The Perils of Penelope Pitstop.
Two King Klongs: The giant gorilla Dick Dastardly hypnotizes in the Wacky Races episode "Real Gone Ape," and the wrestler Bananas the Gorilla becomes in the Help! It's The Hair Bear Bunch! episode "King Klong vs. the Masked Marvel."
Two Bettys frequented the same show in the 1979/80 season on NBC's Fred and Barney Meet the Thing: Barney Rubble's wife, and Benji Grimm's friend in the Thing segments (based on the Fantastic Four character).
The Donald Duck short "Trick or Treat" features a character named Witch Hazel, as do the Bugs Bunny shorts "Bewitched Bunny" and "Broomstick Bunny". Although they were two different characters created by two different studios (Disney and Warner Bros., respectively), June Foray provided the voices for both witches.
Yet another Witch Hazel character appeared in the Little Lulu print comics.
Hey Arnold! and Recess both had a Stinky Peterson. Somewhat awkward with the two shows being quite similar and even sharing a number of voice actors. And while it was live-action, The Red Green Show also had a Stinky Peterson.
And speaking of the Football Head, both Hey Arnold! and Batman: The Animated Series had one-shot antagonists named The Sewer King, who lived in the sewers and had an aversion to light but that's where the similarities ended. Arnold's Sewer King is a crazy kook who refuses to return Grandpa's watch but is mostly harmless. BTAS's Sewer King on the other hand is a dangerous psychopath running his own sick version of Fagin's Gang.
In 1966, around the time the second incarnation of the Doctor on The BBC's Doctor Who was traveling about, Rankin/Bass Productions' King Kong cartoon series on ABC Saturday mornings had a villain named Doctor Who.
Two evil organizations called "M.A.D.": The agents on Tom of T.H.U.M.B. (segment of the 1966 King Kong cartoon—acronym meaning "Maladjusted, Anti-social and Darn mean") and the agents of Inspector Gadget (acronym meaningnote according to supplemental material, The Merch or both either "Mean And Dirty" or "Malevolent Agency of Destruction", not to mention Penny's derogatory version).
Thomas the Tank Engine and Theodore Tugboat, both shows about talking vehicles with a similar structure, had a few cases of this. One interesting case is that both have a regular character named Emily, one a friendly great ocean tug, the other a Scottish steam locomotive.
Within the same series, The Smurfs had two Smurf characters going by the name of Nosey: the real Smurf version who appeared in "The Lost City Of Yore", who was named simply because he was nosy, and the Gargamel-posing-as-a-Smurf version who appeared in "The Mr. Smurf Contest", who was named because of the nose.
Speaking of The Smurfs, both it and The Ren & Stimpy Show had an episode called 'The Littlest Giant'. One giant runs away because he has trouble adjusting to a different civilisation, and the other because he is bullied by his own kind.
From My Little Pony: Friendship Is Magic, there's a background pony named Rose (not a Fan Nickname, but actually called Rose onscreen). There's a popular Doctor Who companion named Rose. Given the popularity of "Doctor Whoof", a background pony that bares a resemblance to David Tennant and spawned a ton of crossover fanworks, its kinda surprising the Pony Rose isn't seen more in said fanworks.
All the Pennys listed in the Hanna-Barbera tab above, plus: Inspector Gadget's cute (and smart) little niece, the adorable peanut girl with antlers on whom Gumball has a crush, Bessie's chubby pal on The Mighty B!, a member of The Proud Family, Rudy's pal/love interest on ChalkZone, the imperiled little girl in Disney's The Rescuers, and Sherman's girlfriend in the Mr. Peabody & Sherman movie.
Four with the name Mr. E: Mr. E From Tau Ceti (a Russian import from 1958 serialized under the Cartoon Classics umbrella title), the Ed Sullivan/Mister T hybrid from the Bakshi Mighty Mouse episode "Don't Touch That Dial," a teacher on Recess, and original Mystery Inc. member and present Scooby-Doo! Mystery Incorporated anti-hero.
Three masked figures named Zero: the hero Popeye relates as a bedtime story to Olive Oyl's niece Diesel, the identity of Bushwhack, Badlands Meeney's sidekick, in the Lariat Sam story arc "The Mark of Zero," and the villain who defaces buildings with zeros in the "Mucho Loma" Rocky and Bullwinkle story arc.
Goliath is the name of two talented dogs. One turns into a lion (It Makes Sense in Context) whenever his owner, Samson, activates his magic bracelets; the other can talk, if only to his young owner, Davey.
The U.S. Acres cartoon has a pig voiced by comedian Kevin Meaney named Aloysius, who is in charge of the television industry. In the 2012 film adaptation of The Lorax, there is a man named Aloysius O'Hare, who is in charge of the air industry. Also, both are shorter than the other characters they are shown with.
Aloysius Owl was a character in Terrytoons' Possible Possum shorts.
Also, Roy Rooster shares the same name as a rooster in this joke.
Warner Bros. had three Ralphs: Ralph Phillips (a daydreaming little boy), Ralph Crumden (a mouse avatar of Jackie Gleason's character from The Honeymooners) and Ralph Wolf (a Wile E. Coyote lookalike in Chuck Jones' sheepdog-wolf series).
Two Claudes as well: Claude Cat (from the early 1950s) and the gangster from the 1968 "Bunny and Claude" cartoons.
Gruesome Twosome was the title of a Tweety cartoon from 1945; the Gruesome Twosome were the macabre participants in Wacky Races with their Creepy Coupe.
Felix is both a cat from a classic cartoon series, and a video-game handyman from Wreck-It Ralph. The latter also has Vanellope Von Schweetz, who was probably partly named for Penelope Pitstop.
One episode of Arthur featured a one-shot character named Charlotte Pickles, the name of Angelica's mom on Rugrats.
Terrytoons had two cats under the name Pinhead Schlabotka. The first was a hulking lamebrain in the Mighty Mouse cartoon "Law and Order," and the other was a sharpie criminal in "Police Dogged" (with one-shot character Clancy the Bull).
Two Gastons: Gaston Le Crayon was an obscure Terrytoons character, an impoverished French artist with a Genre Savvy paintbrush; the other Gaston was the chiseled anti-hero of Disney's Beauty and the Beast.
Two named Swifty: the con-man half of the Shorty & Swifty shorts from Paramount in the mid-1960s, and Oil Can Harry's henchman in the Filmation reboot of Mighty Mouse.
Hustle Bear was the leader of the CB Bears. Four years earlier, The Hair Bear Bunch comic book used a bear named Hustle in "The Hibernation Bit" (issue #8, November 1973).
The G1 My Little Pony series had two different characters named Twilight. The first was a Unicorn from the original TV special, who was the inspiration for Twilight Sparkle in Friendship Is Magic; the second was a Pegasus in the episode "Flight to Cloud Castle".