Carved Mark

Want another way to help show what a Yandere, Stalker with a Crush, or how distressed/depressed a character is? Don't just have them hurt themselves or another person. Instead of having them create a random wound, make it a recognizable pattern. This could take the form of a word, letters, or a symbol. The mark chosen usually has some sort of symbolism, like the name of a crush, as way to show just how obsessive the person is. It may or may not leave a scar. Done to another person, then it is torture. If it is done to themselves, then it would be a subtrope of Self-Harm, carrying a lot of the same ideas with added symbolism. Or they Couldn't Find a Pen.

Anime and Manga

 * In Wolf Guy Wolfen Crest the Big Bad Haguro Dou becomes completely and crazily obsessed with protagonist (and werewolf) Inugami. He initially doesn't care about or even think twice about Inugami... until he pushes Inugami too far. Which results in Inugami showing him his true form and scaring the shit out of Haguro. Haguro goes insane from it, and obsesses and stalks Inugami after that, even cutting himself all over his arm and carving the word "Inu" onto his hand.
 * Baccano!: Not the skin exactly, but The Rail Tracer threatens Czeslaw Mayer with torture involving "stripping away each individual arm muscle and doing intricate carvings on the exposed bone."

Live Action TV

 * In Oz Complete Monster Schillinger offers to be Beecher's new cellmate. Beecher accepts the offer from the seemingly helpful Schillinger, but on their first night in the cell together Schillinger rapes Beecher and "brands" him by burning a swastika design into his right buttock.

Music
"Call you every night and hang up/ Gonna carve your name in my leg/ In my leg, oh, oh!"
 * In the Pink music video "Fucking Perfect" there's a girl who carves the word "Perfect" into her arm in the bathtub.
 * The Weird Al sung-by-a-stalker song "Do I Creep You Out?" (sung to the tune of "Do I Make You Proud?") has the lyric:

Comic Books

 * The League of Extraordinary Gentlemen: When the League first encounters Fu Manchu he is writing on someone's back with acid or other corrosive chemical. It establishes that he's not a nice guy.

Literature

 * In Stephen King's It Henry Bowers carved the first letter of his name into Ben Hanscomb's belly with a knife, and would have put his whole name down there if Ben hadn't fought back and gotten away. Ben still had an H-shaped scar on his stomach nearly 30 years later to show for it.

Web Comic

 * In the webcomic Goblins, the Goblin Slayer carved the word "MONSTER" onto Fumbles' forehead.

Film

 * In the 1996 movie Fear David carves the name Nicole (the girl he's Yandere for) into his chest.
 * In Harry Potter Bellatrix tortures Hermione by carving the word "mudblood" into her arm.
 * Played with when Umbridge has Harry use a special quill to write down "I must not tell lies" onto a piece of paper but it magically carves the sentence into the back of his hand.
 * In Harold and Kumar, Neil Patrick Harris brands his initials on prostitutes.
 * The swastikas carved by the Inglorious Basterds in the foreheads of their surviving victims.

Web Original

 * To Write Love On Her Arms - Renee cuts "FUCK UP" on her arm.

Western Animation

 * Family Guy: Adam West branded his initials on Meg's ass. It's interesting to note that they were once in a relationship.

Real Life

 * Richey Edwards and his infamous 4REAL incident.
 * A woman became internet famous when she said she was attacked by a Scary Black Man who carved the letter "B" for Barack Obama into her face. Turns out she was faking, and part of how it was proved was that the "B" was backward because she did it in a mirror.