Xenilla/Spacegodzilla is very insistent on calling the Crystal Empire royals what they are
Xenilla: I'm eager to see this.. crystal empire of yours, Empress.
Xenilla: Considering the architecture of your land Consort-
Shining Armor: Prince.
Xenilla: -Prince Consort.
Grand King Ghidorah gets pissed if anyone just calls him Ghidorah.
The species of Gods and Demons in Divine Blood were named such by the humans.
Morrigan: I've never claimed to be the Creator of the universe. We started to interact with you, and you called us 'God'. Eventually we just kept having to respond to that and it became the name of the species. As far as I am concerned, the definition of 'God' is my species. And since I am a member of my species, I am not a false god.
In Horseshoes and Hand Grenades,, Jormungandr does not hand out "contracts", but "blessings". JK states it doesn't matter—Jormungandr would just take over him no matter what he called it.
In Potter's Protector Rowena Ravenclaw's magical echo is quite insistent that the diadem she created is not a tiara.
In Raptor, Harry Potter is very insistent that his raptor pack is trained, not tamed; the difference is both distinct and critical. An important example of the difference is shown when Dr. Wu shows his back to Talon despite knowing she doesn't like him. Talon leaps at him and only Harry keeps her from killing the man.
In A Skittering Heart a Worm/KingdomHearts crossover, after Assault forgets Taylorís cape name (Portunes) when giving a TV interview after meeting her he calls her Keynote. Everyone subsequently calls Taylor Keynote despite her attempts to correct them.
In Superhero RPF mentioning that Loki stole someone's power, will be corrected by little old him, that he just borrowed it. Interestingly he doesn't have a problem with the word steal in any other context.
In the Elizabeth Quatermain universe, Elizabeth's father Allan narrates the events from his own separate side volume, in which he refuses to refer to Elizabeth and her half-brother Harry as anything other than Daughter and Son. In the main storyline, meanwhile, Skinner has a good half-dozen nicknames for Elizabeth, but uses her real name only once.
An Alternate Keitaro Urashima: After realizing that Haruka's supporting Granny Hina's manipulative attempts to force him to take over the Inn, Keitaro starts pointedly calling her Aunt Haruka, much to her frustration.
In Harmony Theory, Rainbow Dash finds herself a thousand years in the future. Cutie Marks are now called Talent Glyphs. Rainbow adamantly calls them Cutie Marks, claiming Talent Glyph just sounds wrong.
In The Immortal Game, many characters repeatedly state that "titles are important". The best example is Esteem, who uses it so much that it's practically his Catch-Phrase (considering the character, it's probably to remind everyone that he's both a knight and a General).
In This Bites!, Cross objects to being called a kid or brat, being 18. He also objects to Vivi's nickname for him, Mister Jeremiah, which comes across as implying he's much older than he is. The insistence ends in Chapter 18, when he finally gives up.
In Fighting for the Future, Luffy spends quite some time insisting he's simply a "concerned citizen". As a result, after beating Arlong he's in the paper, not as the newest bounty, but being hailed as a hero for taking down such dangerous threats.
A lot of things are called demons in Goddess Reborn Chronicle-in English-speaking countries, if they're demons or not. It's noted that English lacks a good word for what to call them as a collective whole. This is, of course, present in the original works as well.
It's fortunate, he thinks fuzzily, just before dreams usher him away, that Fate decided to present one mostly-deserving captain with two such trustworthy subordinates-and-friends. Oh, who is he kidding. He is a very lucky man, and he knows it.
Eugenesis takes a moment out of the narrative to note that Straxus used to insist the Harvester Units (machines designed to find bodies and take them to the smelting pools to be melted) were Sanitation Units.
In X-Men: Revolution (Which has since been renamed), Betsy Braddock repeatedly insists on being called 'English, not British, its a common misconception' whenever someone refers to them as the former. This was because two readers complained about the stereotypes used in characterizing her and any non-American characters used, with one telling them that 'British' is an incorrect term, especially when referring to them, and she rewrote the entire story to remove the stereotypes, and for her added this. Betsy's brother Brian, however, doesn't have a problem being referred to as 'Captain Britain', due to it being his self picked title. Ironically, Betsy once served in the role.
By the end of the Stars From Home series, Scott is Happily Adopted and won't let anyone refer to Chris Summers as his dad. Charles is his dad, Chris is his father. (He does relent and let Ororo refer to Chris as his "back-up dad".)