Most of the Safety Patrol on Fillmore! refer to each other by last names, despite being middle schoolers. (Though if your first name was Cornelius, wouldn't you want to go by Fillmore?) Ingrid is usually called by her first name, but not always.
Don't forget (Turanga) Leela, although it's implied "Turanga" is her surname, in which case, this would be an inversion. (In another episode, her parents are referred to as Turanga Morris and Turanga Munda, further implying that mutants arrange their names surname first - though Leela was not aware she was a mutant, it seems she may still have arranged the name that way.)
In one of the movies, the mailbox outside of Leela's parents' house reads "Turanga".
This is lampshaded in the episode that introduced their full names, as seen in the page quote.
Mr. Burns from The Simpsons, in that his first name (Charles) is hardly ever used. When people wish to refer to him informally, he goes by his middle name, Monty.
Given how Mr Burns was adopted by an eccentric old billionaire as a child, is its possible he was named after the Roman convention where Charles would be his pre-nom and Montgomery is his actual name (for example, Gaius Julius Casaer). Given how old-fashioned, eccentric and high-society he is, this would make a lot of sense.
Except Roman names don't work like that. Julius is Caesar's family name, and Caesar is the nickname of an ancestor that was adopted as the family branch name. It seems more likely he has a European style name, in which there is no "middle name" but rather a series of given names, one of which is the basis of the personal name.
Smithers is also rarely referred to by his first name, Waylon.
Homer calls Ned Flanders by his last name.
Justified in a Flashback when Ned introduces himself to Homer the day the latter moves into the neighbourhood, and having immediately rubbed him the wrong way by being himself, says
Flanders: Hi-diddly-hey, new neighbour-ino. My name's Flanders, but my friends call me Ned!
Her employer Dr. Drakken (real name Drew Theodore P. Lipsky) is usually addressed or referred to simply as Drakken. The same applies for one of the other villains, (Duff) Killigan, and for Kim's teacher (Steve) Barkin.
Also, Mr. Barkin addresses students by their last names; it seems to be a mix of formality and gruffness.
The commander of Titan Maximum is called Palmer. Even his grandparents call him that, while his far-less-cool little brother is just Willie.
Oddly enough, there were a few moments in Rugrats where Angelica would address Tommy as "Pickles," despite the fact that they are cousins and share the same last name.
"Once-ler" is implied to be a surname in The Lorax 70s special.
In The Mr. Men Show, various characters (usually Mr. Grumpy) sometimes refer to a Mr. Man or Little Miss without saying "Mr." or "Miss."
Commander Hoek, although he doesn't mind simply being addressed "Ren".
Rook Blonko is this way, but that's because his name is introduced with the surname first. Seeing as he is sent to Bellwood in America, and his race don't seem to leave their planet often, it could quite possible have been a mistake Ben and everyone's part, thinking they were calling him by his first name.
Ulrich, Jeremie and Odd of Code Lyoko are this way in X.A.N.A. Awakens. It's implied Ulrich and Jeremie are this way due to their different social classes at Kadic though no explanation is given for Odd falling victim to it.
During the last season of Daria, Jane would occasionally call Daria by her last name, Morgendorffer. Usually, she was just teasing.
Jimmy and Cindy from The Adventures of Jimmy Neutron usually call each other by their last names as a sign of their rivalry. Come the episode "Stranded" Cindy calls Jimmy by his first name as the two get closer, surprising Jimmy and later Carl, Sheen, and Libby. To the point where Jimmy mentions that he wasn't even aware that Cindy knew his first name.