On Murphy Brown, Corky Sherwood married a man whose last name was Forrest, making her married name Corky Sherwood-Forrest. Rather amusingly, the actress who played Corky, Faith Ford, was married at the time to a man whose last name was Nottingham.
On the BBC's Wings, Lieutenant Gaylion's surname is pronounced GAY-lee-un. For much of the first season, Captain Triggers refers to him as gay-lion, pronouncing it as though he were a predatory cat that prefers the company of other male predatory cats.
The name Robin Charles Scherbatsky Jr is the king of this trope. Why? Because the name belongs to a woman.
The show gave us Theodore Evelyn Mosby. Evelyn used to be a male name. Barney tried to use Ted's full name and used "Theodore Vivian Mosby".
One episode has a poor girl named Cook Pu. Ted unfortunately thinks that this is a prank name his students edited onto his attendance sheet in order to make him look stupid, and goes about mocking them at length for not having enough imagination to come up with a name less lame and obvious than "Cook Pu". He does feel terrible when he realizes that it's actually a real name — when the student in question runs out of his class in tears. Oops.
Lily and Marshall gave their son Marvin the middle name Wait For It as a reference to one of Barney's catchphrases. Barney chose the name himself. The gang thinks it's awesome.
A ship full of alien refugees with difficult names arrives on Earth and all are assigned human names. Naming thousands of people can get pretty tedious, so the ones near the end of the line ended up with names like Sam Francisco, Rudyard Kipling, etc. The names were somewhat difficult but not prohibitively so: George Francisco (formerly Sam) was Stangya Soren'tzah and Cathy Frenkel was Gelana Vray, for example. The names were selected not only for absurdity or evocation of famous humans, but also with irony or malice: a not-so-bright Tenktonese was called Albert Einstein, and a couple interested in having an electric articles store were named Thomas and Alva Edison. And, strangely, years after the descent, the immigration office still is funny with names: in the TV movie Dark Horizon the newly arrived Aphossno is named Norman Conquest.
The film was implicitly referencing Ellis Island clerks who "Americanized" immigrant names they had trouble pronouncing this was probably intentional. The clerks weren't even smart enough to turn Stangya Soren'tzah into Stanley Sorenson.
In the movie the series was based on (thus making it not The Film of the Series) Sam Francisco comments to Sykes (after he had said Sam's name sounded embarrassing) that "Sykes" sounds like the aliens' word for "shithead".
Marcy Rhodes takes the news that she got married to a man she doesn't remember meeting in a ceremony she also doesn't remember surprisingly well... but she's much less pleased to learn that her name is now Marcy D'Arcy.
Once, Peggy and the kids are going through the phone book looking for a new last name. Perfectly good names keep getting rejected because Kelly can't spell them. So they end up using "Cat". Buck was especially thrilled. (Cat being an odd choice, as another episode shows that Kelly can't even spell that right.)
The generally unfortunate Doctor Who companion Peri Brown's real first name is Perpugilliam. (Yes, she's from Earth.)
A sketch called "Mr. and Mrs. Git" had a family with the surname "Git". They had "A Sniveling Little Rat-Faced Git" and his wife "Dreary Fat Boring Old Git". The Gits had named their children "Dirty Lying Little Two-Faced" and "Ghastly Horrible Spotted Vicious Little". They do recognize that it's unfortunate for them to have a surname like "Git", but given their horrible first names they recognize that changing it won't do them much good. Then again, as the sketch goes on you learn they're actually quite horrible people to go with the names, so it's all... Ok?
Mr. Smokestoomuch. Apparently it wasn't a burden, he was well into adulthood before he figured it out.
Raymond Luxury Yacht, which is actually pronounced "Throat Warbler Mangrove."
Mrs. B.J. Smegma of 13, The Cresent, Belmont from the sketch "How Not To Be Seen".
There is a U.S. sitcom writer with the name Mike Haukom (whose worked for shows like Everybody Loves Raymond and Rules of Engagement); not 100% sure if his last name supposed to be pronounced like "how come" or "hawk 'em", but if pronounced as the latter, it has a similar effect if said real fast.
Finn and his pregnant girlfriend Quinn discussing baby names:
Finn: And then I thought up the perfect name - DRIZZLE!
In another example from this series, of the Unfortunate Meaning variety, one of the girls from the Jane Addams Academy is named Aphasia.
Love Connection introduces a 26-year-old man who loves beer and loud music. He currently works in gift sales and his mom seems to have some issues with his love life. Ladies and gentlemen, Robert Fagot.
It had one contestant called Steve Raper. To make matters worse, he represented the University of Bath, so every time he buzzed in The Announcer said "Bath Raper", which sounds like a Serial Killer sobriquet.
Martin Heighway (pronounced "highway") of the Open University: "Open Heighway".
A subplot in Hill Street Blues had Det. La Rue trying to help the career of a struggling standup comic named Vic Hitler, who had made a deathbed promise to his father to keep the family name. La Rue encountered him, not yet knowing his name, and he was so funny La Rue was cracking up laughing. He couldn't understand how this guy couldn't make it as a comic. Then he learned his name.
Stringfellow Hawke, of Airwolf. Perhaps one of the most memorable names of all TV characters. He gets to share a laugh with one Michael Coldsmith-Briggs III over each other's names.
One episode of Cheers had Carla trying to get around a family naming tradition that would have unintentionally forced the name "Benito Mussolini" onto her unborn baby.
One episode of Miranda featured both a character called Susan Perb (Sue Perb = superb) and a character called Dick Twist (which needs no explanation). When Miranda's new work colleagues don't find the former funny, it's the final straw and she quits the job; the latter becomes a Running Gag throughout the episode.
Captain Darling from Blackadder Goes Forth. The creators said that as soon as they came up with the name for him, he went from a totally empty character to one who'd been steeped in a lifetime's worth of bitterness and resentment from being called "darling" by everyone.
Malcolm in the Middle: A girl in Dewey's class at school is called Regina Tucker. Reese is still unable to think up a sleazy nickname for her.
The Malaysian government tried to ban Power Rangers because their title "Mighty Morphin'". And morphine is a drug.
While not treated as such in-show, Captain Hunnicutt of Mash arguably has one of these in "BJ". You may think that the modern connotation of that initialism probably hadn't been developed yet in The Fifties, but there is a scene in one episode that offers a possible nod-and-a-wink to this. A visiting nurse asks Hunnicutt what BJ stands for. Before he can answer, Hawkeye quickly interrupts with, "Anything you like." Another episode, however, has him explain that he was named for his parents, Bea and Jay.
On Bones Angela's given name was so terrible that she changed it the minute she turned 18. While we don't know what the name was, we can assume it was pretty bad being as she wouldn't let her husband hear it, her father wanted her to name her son Staccato Mamba, and, most importantly, her middle name is "Pearly Gates."
In a bit on The Daily Show, before he left for his own show, Stephen Colbert confessed that his name was Ted Hitler. "No relation. Okay, well, distant relation. Two generations. Straight up. Okay, Hitler was my grandfather!"
In Keeping Up Appearances the main character, an inveterate snob, is Hyacinth Bucket, though she insists on pronouncing it Bouquet and gets very stroppy when others call her Mrs. Bucket. Her husband, Richard, from whom she obviously got the name, is not embarrassed by his surname at all and tends to roll his eyes when he hears her correcting people.
In 3rd Rock from the Sun, Dick learns that he is the Big Giant head's son, which would make his surname "Head."
In one episode of The Goodies the gang has to market a brand of bedtime drink that they rename 'Snooze'. The original name of the product? Venom.
One skit from Chappelle's Show featured a 50's style sitcom about the Niggar family, who are actually white. Much fun was had with N-Word Privileges. The end of the skit has them meeting a hispanic family named the Wetbacks.
Angel had a recurring demon character who was called either Lorne or just The Host, due to his running a karaoke bar. That's because his real name was Krevlorneswrath of the Deathwok Clan. In the episode "Belonging", he explains that he considers just Lorne to still be an Unfortunate Name because of the Bonanza jokes (he has green skin, and Bonanza stars Lorne Greene). In his home dimension of Pylea, "The Host" is also an unfortunate name as it is more closely associated with parasites than guests there.
In the Grimm episode "Nameless", a Fuchsteufelwild traditionally has a name that is an anagram of Rumpelstiltskin. The Fuchsteufelwild responsible for the murders is stuck with the name Trinket Lipslums.
Good Luck Charlie has PJ Duncan, who's name in one episode is revealed as Potty John. Then it gets changed to Patty John, legally PP Duncan. Poor guy.
In a sketch in Man Stroke Woman, a couple talks to another couple about them having a baby and what they plan on naming it. They apparently plan on naming it Crapbasket. The other couple resists their urge to say something, and tell them it is a lovely name.
In season 6 of Sons Of Anarchy, Wayne Unser sometimes babysits Abel and Thomas in his trailer and has been given the nickname Uncle Touchy.
Wayne Unser: You know that nickname makes me sound like a pedophile.