DSBT InsaniT: From episode 3 onwards, the creator is not referred as 'Vexusdylan', but 'Vexusdylan DA SECOND'. Andy is usually the one to enfore this rule.
In Echo Chamber's "Trope Of The Week" episode Unresolved Sexual Tension Dana and Tom are trying to discuss their characters separately from themselves, in order to keep themselves distant from their roles. It leads to a lot of "I will... I mean she will..."
The leaders of the seasteads in In Golden Waters prefer to be called "captains of industry" and not pirates, slavers, or robber barons.
It also applies to Old Man's brother... who is also named "Old Man".
The crew of Linus Tech Tips refer to hoverboards as "swegways", due in part to their similar method of operation to the segway.
In Lovelace ½, Andi is "Miss Gannett-Moore", not "Miss Moore" or "Miss Gannett".
In Triumphant Return! by Matt Santoro, Matt says that he got some "cool social media cards" made for him. Big Shine says that they're "business cards". Matt corrects him, explaining that they don't have any personal information. Big Shine gets even madder, and knocks down Matt.
The fans of Mike & Tom Eat Snacks are not viewers. They can't be after all. What they are is debatle, but they are not viewers. Whenever Mike or Tom make that mistake the other one corrects him.
Tasakeru: The intelligent mammal species are called "sentients". Only non-intelligent species are referred to as "animals".
Tobuscus' friend, Gabe, would like everyone to know that his nickname is "Gabe-uscus", not "Gaybuscus". Too bad Toby insists on pronouncing it without the pause. Parodied in Tobuscus Animated Adventures when he insists on the pronunciation even as Zombie!Toby is eating him.
In Welcome to Night Vale virtually everything is referred to the same way every time it comes up and nothing is ever shortened. Some examples include:
"John Peters, you know, the farmer"
"Larry Leroy, out on the edge of town"
The Faceless Old Woman Who Secretly Lives In Your Home
Wheat and wheat by-products
The Desert Flower Bowling Alley and Arcade Fun Complex
Hiram McDaniels, who is literally a five-headed dragon.
The Shape in Grove Park that No One Acknowledges or Speaks About
Larry Damone, in the Whateley Universe, is a mutant with the codename "The Man Called Vengeance". He can't get people to stop calling him just "Vengeance". His team leader Fantastico calls him "Vengie", which really bugs him.
The school administration adamantly puts it's foot down when people call Whateley Academy a Superhero School; they have a strict policy of neutrality to uphold, after all.
In the Jake and Amir episode Staycation, Amir insistently calls the trip to Mexico he booked a "staycation" despite that not being what the word means.
In Dragon Ball Z Abridged, when Cell calls Android #17 and #18 "Cyborg", Piccolo tells him that they call them "Androids". Cell responds with "Well, good for you; you're wrong!"