In the Aubrey-Maturin series, when HMS Surprise is bought from the Navy, Jack Aubrey hates it being referred to as a Privateer, which were seen as little more than legalised pirates. He prefers the term "Letter of Marque" or "Private Man-o-War".
In The Book of Wizard Craft the narrator refers to sea monsters as "Physically Gifted Marine Presences" in the section about them because he believes it's more politically correct— he catches himself calling them "monsters" once after introducing the term and immediately apologizes "Er, I mean presences."
From The Lotus Eaters: in the Republic of Gaul's navy, "There is 'My God' and 'My ass', but there is no mon capitaine."note "My captain", in case anyone was uncertain.
The Mort book has Mortimer, who, whatever the topic of conversation, would reflexively correct anyone who called him "boy" or "you" by giving his name. In the final duel this becomes a Berserk Button.
From Making Money, Unseen University has a Department of Postmortem Communications, who summon the spirits of dead people to talk to them. They are not "necromancers". Necromancy, in fact, is strictly forbidden at Unseen University!
From Unseen Academicals, the Bengo Macarona football chant, adjusted (at Macarona's insistence) to include all his academic appointments and titles. An Overly Long Gag as well, since after a couple repetitions the list has gone on for two pages. Worth slogging through if you like puns.
Ankh-Morpork's Guild of Seamstresses prefer to be known as the "Ladies of Negotiable Affection". 'Not prostitutes, "Ladies of Negotiable Affection".
Unseen University librarian is an ape, not the M-word. Knowing the difference is part of natural selection.
Miss Susan Sto Helit (the granddaughter of Death).
Mister Vimes, who insists on the title (even after he is technically Sir Samuel Vimes or even the Duke of Ankh.)
Technically certain of his titles override others in proper use, but his some-time ambassadorial attaché insists on introducing "His Grace, His Excellency, The Duke of Ankh; Commander Sir Samuel Vimes"
Rincewind's ability to do magic may well be in the negative territory, but he is a wizard, okay? It says so on his hat. With two z's.
The Assassins' Guild do not kill their targets. They inhume their clients.
In Everworld, Sobek insists on being addressed as "Sobek, god of the crocodiles of the Nile, called Rager, son of Seth and his consort Neith, nurse of the crocodiles". As he's a living god with thousands of crocodiles at his command, no-one disputes it.
There was also a "I am not Belgian, I am FRENCH!" moment, followed immediately by "My apologies. Correcting people has become a reflex."
In The Hitchiker, a short story by Roald Dahl, the titular hitchhiker insists that his profession is "fingersmith" rather than a "pickpocket". He's an artist, as skilled in the use of his fingers as a blacksmith is with metal, not a common criminal who robs blind old ladies.
In a bit of an inversion, when Bilbo Baggins balks at getting hired as a "burglar" in The Hobbit, the dwarves miss the point and tell him he can be an "expert treasure hunter" instead.
In Idlewild, Halloween repeatedly defends that he is not a necrologist, he is a thanatologist.
Left Behind: Captain Rayford Steele. Always Captain Steele. While the character doesn't explicitly insist on it, the author is very careful to write his name this way when being addressed by others.
The Kzarchians from Invasion Of Kzarch all have apostrophes in their last names, and they insist on that apostrophe being pronounced, although no-one aside from them can tell the difference. Also, Bloody Jack insists on being called Bloody Jack, for some odd reason.
The titular character in Anne Rice's Memnoch the Devil insists that Lestat call him "Memnoch", not "The Devil", Satan, Lucifer, or any other names the humans have come up with for him. Besides, all those names carry with them certain preconceptions, and Memnoch would rather Lestat let him tell his story from a fresh perspective.
Peter Grant would like you to know that it isn't Black Magic, it is Ethically Challenged Magic, thank you very much.
Aahz, of Robert Asprin's Myth Adventures books, is a demon from the dimension called Perv, and quite firm about the correct term for his race being "Pervect", not "Pervert", the latter being a racial slur.
In the comic book adaptation, Aahz's apprentice Skeeve correctly addresses another Pervect, who starts to scream at him... then stops, astonished to realize someone actually got it right, and asks politely what he can do for Skeeve.
It's all especially funny because all racial terms in the books are insults. Skeeve, for example, is a Klahd because he's from Klah, and the characters from Trollia are Trolls or Trollops, depending on sex. Pervects are thus asking for respect that no one else gets. Then again, they are Pervects, so they mostly get it.
When Sara of theOrigami Yodaseries brings the Fortune Wookiee, a cootie catcher version of Chewbacca, to school, Harvey's comment on the chapter is literally nothing but a remark on how it's a "salt cellar", not a "cootie catcher".
In the 4th book, Dwight insists that Cassie call him "Captain Dwight".
From Pandora's Star: It's a flow wormhole generator, not a hyperdrive.
Also, a slightly more meta example: Peter F. Hamilton never misses a chance to remind you that the concrete is enzyme-bonded.
In the Redwall series, hares do not like to be called "rabbits". If the hare has a short enough temper, you may get beaten up for calling them a rabbit repeatedly. This is actually a justified instance, though, because most rabbits in the series are portrayed as stuck-up, prissy weaklings while most hares are soldiers. They're also world-class goofs, so they probably object just as much to the implication that they don't have a sense of humor. There is a distinction between hares and rabbits in real life, so there's that too.
In The Southern Reach Trilogy, the twelfth expedition into Area X discovered a buried structure, which most of the members describe as a "tunnel" but which the biologist insistently refers to as a "tower".
A minor Running Gag in Star Carrier: Earth Strike has the Book Dumb Marine Lieutenant Ostend trying to describe the native wildlife of Haris in terms of Earth biology (e.g. spiders), and getting corrected that, no, the terms he's using don't really apply except as a rough simile. One of his more learned compatriots uses the term "florauna"* portmanteau of "flora" and "fauna" because it's the closest English can get.
In The Thrawn Trilogy, Thrawn refuses to acknowledge the New Republic as anything other than "The Rebellion", although the trilogy took place five years after Return of the Jedi, by which point Coruscant itself had been retaken. This is a case where changing the name of a thing changes the thing itself. The New Republic is a foreign power. The Rebellion is an uprising of Imperial subjects. In the same way, Abraham Lincoln never called the states in secession from the Union by the name "Confederate States of America".
The Hand of Thrawn Duology has Grodin Tierce, part of the triumvirate who are collectively endeavoring to make it look like Thrawn has returned, once talk about The Rebellion, despite this taking place ten years after Thrawn's death, by which point the New Republic is a Galactic Superpower and the Empire has been reduced to a single sector in size.note That's still over a thousand inhabited star systems, though. Normally he just calls it Coruscant, which is its seat of power; he never calls it the New Republic and calls it the Rebellion exactly once. This is one of many little bits of Foreshadowing, because Tierce is a clone who was specifically grown as an attempt to make someone who thought like Thrawn.
In Iron Fist, while suffering her first pangs of Double ConsciousnessLara Notsil repeatedly catches herself thinking of the anti-Imperials as New Republic forces, and with vehemence corrects herself, Rebel forces.
When the Old Republic became The Empire, the capital planet Coruscant was renamed "Imperial Center"; though a number of characters, even Imperials, complain about this, some use the term exclusively and don't like hearing the old word. When the New Republic takes the planet back, they change the name. They try to change the name of the Imperial Palace, where the seat of government had been ever since the Senate building had been torn down, but none of their alternate names stick.