Hey, we aren't "describing" Insistent Terminology, we are "articulating" it!
A character constantly corrects a word (fine, if you say it's called a term, then it's called a term) used in their introduction or any speech that otherwise refers to them, but never seems to stop (all right, keep) anyone else from using it. Sometimes this is because they could be called something people see as unflattering or a poor choice of words.
Occasionally this extends into a species joke, where an alien or funny animal corrects others about some stereotypical aspect. Can also be done with an ethnic joke where the person has to correct others about some stereotypical aspect of nationality.
Subtropes to this are as follows:
Action Figure Justification: It's not a "doll", it's an "action figure".
"Blackmail" Is Such an Ugly Word: Character insists on a euphemism to cover up a negative reality.
Distinction Without a Difference: Character insists on a synonymous term.
Less Embarrassing Term: Character insists on calling something by a more "dignified" term.
Spell My Name with a "The": The character insists on an article to impress.
I Am Big Boned: Character insists their weight problem comes from an uncontrollable source.
Not Using the "Z" Word: Usually a meta-example, because the work itself refuses to use a colloquial term.
It's Not Porn, It's Art: The distinction between art and porn is debated.
Would Be Rude to Say "Genocide": Character insists that certain actions are actually not genocidal.
Never Say "Die": Usually a meta-example, often due to Moral Guardians opposing any mention of death in children's media.
Technical Euphemism: Using technical language to make something seem less disturbing or gross.
Compare/Contrast with She Is Not My Girlfriend (character insists a romance does not exist, sometimes an overlap when "friend" is substituted), Do Not Call Me "Paul" (character has a name they do not wish to be known by), Blatant Lies (character insists to make an affirmation that obviously isn't real), Don't Call Me "Sir" (character insists another not be formal), They Call Me MISTER Tibbs! (character insists another uses a formal/informal title in conversation), You Keep Using That Word (a character corrects or points out another character's repeated word misuse), Pronouncing My Name for You (when a character insists on others getting the pronunciation of their name correct/the way they want), and Pretentious Pronunciation (character wishes to class up something by "pronouncing it poshly", overlaps if they insist on their pronunciation).