AKIRA: Almost all of the dialogue between Tetsuo Shima and Shotaro Kaneda will be prefaced with the protagonist and antagonist screaming each other's names. "Tetsuo!" "Kaneda!"
These are listed as "memorable quotes" on IMDB. So memorable, in fact, that quoting it on any forum or Image Board will inevitably lead to a whole thread of people quoting other examples of this trope; if it isn't used first, it will pop up eventually.
Ashita no Joe, where everyone and their mom scream Joe's name at one point or another.
Katekyo Hitman Reborn!: JYUUUDAAIIMEEE!!!! There are actually entire compilations of all of Gokudera's "Jyuudaime"'s. It's very long. (Did we mention that that compilation was only for roughly about slightly past half of the anime?)
Many fans got their first taste of the anime-style of this with Fushigi Yuugi: "Miaka!" "Tamahome!" until it became a meme associated with that show.
Suboshi quite a bit in the fist OVA series: "Yui-sama! Yui-sama!!"
The 1970s series Candy Candy delights the audience with a scene where Candy and her best friend Annie are reconciled. A few minutes of "Candyyy!" "Anniiie, oh Annie!" "Candyyy!" "Annie!" "Oh Candy!" ping ponged with such strong feeling that (at least in the Finnish dub) you can close your eyes and see something else than little girls running towards each other on a meadow of fragrant blossoms and sparkling dewdrops.
Ginji greets all of his friends (even Punch Clock Villain Maguruma!) by going Super-Deformed, calling their name and waving a fan with the kanji for "happiness" on it.
Kazuki's "JUUUBEEEI!" in the first Infinity Fortress Arc when Juubei looks on the verge of death after his battle with Kazuki. The manga artist took the liberty of devoting almost a full-length page to the speech bubble.
Emishi's "SHIDO-HAN!" speech bubble when it looks like Shido's been killed by Liu Mengyan's flunkies is almost that big.
In the manga, Ginji greets Shido and Makubex respectively after his first time seeing them in ages: "Shido! Shido! Shido!" "Makubex! Makubex! Makubex!"... both multiplied by a few more times.
Cardcaptor Sakura anime has an elevator scene with Syaoran and Sakura. Syaoran yells "SAKURAAA" as she plunges into the depths of wherever. Since this is the first time that Syaoran's ever done this instead of using his usual dismissive Hey You, it's a sign of Relationship Upgrade.
Nagi of Hayate the Combat Butler calls out Hayate's name whenever she's in trouble, as does Nishisawa once or twice. He will always appear immediately out of nowhere to save the day once so summoned; on at least one occasion he even apparently waited out of sight until Nagi called out his name before saving her from a rampaging robot.
InuYasha: "INUYASHA! KAGOME!" This show takes name-yelling to new heights. Mercilessly parodied in a commercial for the show, with moments taken from all across the series' run. Which can be seen here.
In Kikyou's debut sequence, her name was six or seven of Inuyasha's lines in a row.
Inuyasha says Kagome's name 568 times in the whole series, while Kagome says Inyuasha's 971 times—the majority of both being screams. Out of 167 episodes.
"RANMA!!! AKANE!!!" moments are very common in Ranma ½, Rumiko Takahashi's early work. Played for laughs when the normally belligerent Ranma and Akane turn into Sickeningly Sweethearts because of love mushrooms. Instead of using their actual names, they call out to each other using terms of affection.
Taken to the extreme in the teaser trailer for the third movie revolving around Ichigo and Rukia. All Ichigo screams is RUKIA! In the most anguished and dramatic way possible. The movie is actually tagged as "Fade to Black; Call out Your Name".
By the end of the Soul Society arc most of Rukia's lines consist of "Ichigo!!" "Renji!!" "Nii-sama!!"
"HINAMORI!" seemed to be Toushirou's catchphrase at a certain point in the manga.
Orihime notoriously repeats "Kurosaki-kun!" throughout the Hueco Mundo arc. During the end of the Lust mini-arc, the original version of the manga makes clear that it's a kind of Madness Mantra ( she was calling out to Ichigo who had been pretty much been been killed in front of her), in a way that no other medium, not even the original version of the anime, could do. Normally, Ichigo's name is written in kanji, but when Orihime just starts chanting it, she does so in hiragana.
Yamamoto gets in on the 'calling names out loudly' trend in a less dramatic manner when he sees Ukitake and Kyoraku fall after consecutive attacks by Wonderweiss and Starrk.
Taichi and Yamato knock each other off a cliff in one episode. Taichi manages to grab on to the cliff with one hand while Yamato grabs onto him with one hand. Say My Name ensues.
Digimon Adventure does this kind of thing a lot, several of the first evolutions to Champion level (at least) were proceeded by a round or two of Say My Name between the kids and their partner digimon.
Heroic Age: In any scene in which she appears, Princess Dhianeila will say "Age," (pronounced "Ay-ee-gee") the name of the Wild Child protagonist. Problem is, given the insane level of telepathy she has, it's entirely possible that she is contacting him directly, though no evidence of this is ever shown in the series.
Shinji does name-saying in his dreams. Shinji has a LOT of these moments, and it spells out a lot of how he relates to various people. Asuka is the only one he's on a first-name basis with (even calling for help).
Adults get (first name-san), Rei is always just Ayanami, Kaworu is "Kaworu-kun".
SASUKE! Gaara calls him "Uchiha Sasuke" so many times while the two of them are fighting (both whispered and shouted) that you could make a drinking game out of it, as at least one episode reviewer observed.
Screaming after the fight after the Chunin exams: "NARUTOOO!" "SASUKEEE!"
'Sasuke-kun' was young Sakura's catch-phrase? Half her dialogue? She said it so constantly for so long that any of her voice actresses must have either been writhing or taking it as a personal challenge to find out how much variety they could get out of this one line over and over and over again.
The Guardian Ninjas filler arc has Asuma and his enemy and former friend Kazuma yelling each other's names a lot, and Naruto often yells Sora's name.
People yell Asuma's name quite often around the time that he dies.
There's Hinata's "Naruto-kun...", although it's rarely shouted.
Lampshaded in an omake in Shippuden. Kakashi teases Hinata about her stammering "Naruto-kuns", being a big hit with the male viewers. That inspires Sakura to launch into a long litany of "Naruto-kuns" herself, as Kakashi and Hinata call out different moods for her to act out with each one.
Judai from Yu-Gi-Oh! GX had always been incredibly fond of saying peoples' names, but when it came to Johan, he really pulled out all the stops. Poor Asuka's lines in all of seasons 3 and 4 were reduced to her just saying "Judai..." in moments when it looked like he was in a tough corner, and "Judai!" when it looked like he was in serious trouble.
"SHANA!!!" "YUJI!!" Actually of plot importance, because Shana got her name from Yuji, and Yuji is usually not referred to with his name by the Flame Haze, because they consider him an object rather than a person.
Played with when Batou yells 'MOTOKOOO!', only to later find out she's perfectly fine, and the other Section 9 members tease him about it.
In The Movie during the climax when [the Puppet Master's body is blown to hell and Motoko appears to have died after merging with him. She gets better after finding a new body.
Used in the Stand Alone ComplexPS2 game, where the antagonist had a cybernetic body that had the exact same specs as the Major's own. Batou singled out the impostor by yelling "MOTOKOOO!!!" and shooting the one that reacted.
The Major: "So, how did you know that that wasn't me?"
Batou: "I just knew... Besides, you'd never react just 'cause I called out your name."
Used often in Princess Tutu, particularly in two climactic scenes in the second season. Some fans were jarred when the dub's decision to translate the main character's name to keep Theme Naming meant that Fakir screams DUUUCK! in one such scene.
The scene where Daisuke calls Riku by her name when he tells her he's in love with her, not her sister Risa. Up to that point he'd always called both of them "Harada-san", prompting her to angrily complain she can't tell which one of them he's referring to. He still uses "-san" to a girl he's going out with, and she still calls him "Niwa-kun".
Vandread: At the absolute end where, for the first time in the series, Hibiki calls to Dita by her name.
It becomes sad in the Shimabara filler arc, when as Magdaria lays dying in Sanosuke's arms, Sano realizes that she never told him her real name and mentions it in tears. Sayo smiles weakly and says "Sayo... my real name, it's Sayo..." and dies less than a minute afterwards. Sanosuke spends the following seconds holding his deceased friend (maybe) in his arms, whispering "Sayo... I'm so sorry, Sayo..."
Episode 10 of R2 has The Chessmaster Lelouch one-upped on the battlefield by Xingke. Cue XIIINGKEEE!
By breaking the laws of writing through the sheer Power of Awesome, Jeremiah Gottwald says his own name:
Jeremiah Gottwald: You can't hit me! JEREMIAHGOTTWAAALD!
In One Piece, whenever a character gets injured in a battle that other crew members are watching or participating in, someone close to them typically yells their name. Examples include:
Sanji yelling his female crewmates' names
Nami yelling Robin's name
Robin yelling Chopper's name.
When Usopp is disguised as Sogeking in desperate situations, his crewmates yell out his real name, rather than his assumed one, even though they're playing along with his masquerade (with the exceptions of Luffy and Chopper, who can't see through his Paper-Thin Disguise).
Ash seems to yell "Pikachu!" or "TEAM ROCKET!" at least once an episode. Picachu is his faithful pokemon. Team rocket are his adversaries.
This trope's dramatic effect is lost, but it is still used in the Orre games. In XD, it causes the called Pokemon to focus and heighten its accuracy. In both games, it also snapped a Pokemon out of any induced slumber. Most importantly, however, it's one of only three ways to snap a Shadow Pokemon out of Hyper and Reverse Modes, a state not even the Pokemon Center can cure.
In some Victorian Romance Emma episodes, all Emma does is to whisper the name of the person that is talking to her. The manga has a completely different ending, and she can still speak in full sentences there.
Through the course of Arashi No Yoru Ni, Mei and Gabu speak/yell the other's name in times of peril and/or uncertainty.
Lead Shibuya 'All-Loving Hero' Yuuri is king and at the center of everyone's attention, all the time. He gets his name called so constantly that heika!, meaning 'your majesty', is the most common word in the script. He gets it from Gunter constantly, from Conrad regularly, and from Gwendal in extreme circumstances, as well as from random subjects and people he's just met. Conrad also calls him Yuuri in intense situations on and off, depending on how he's feeling, and Wolfram's impassioned exclamations of his fiancée's name are to be counted on anytime anything dangerous happens, like he thinks it'll somehow protect the wimp. Shori is also good for a 'Yuuri' or 'Yu-chan' pretty reliably, and Murata comes out with a good number of dramatic 'Shibuya's.
Yuuri himself does plenty of name-calling. Especially Conrad and especially during the Arm Arc.
There are other instances of names being scrupulously avoided: Murata whenever he goes to talk to Shinou in the temple is a good example, as well as the way Murata and Shori choose to address each other: 'Friend of my little brother' and 'older brother of my friend,' and Wolfram's determined address of his brother Conrad as 'Weller-kyo'.
This last shattered in the scene at the burnt church where Yuuri and Conrad are both missing, presumed dead, and then they find Conrad's severed arm... COOONRAAAD!
This is taken to ridiculous levels in an issue of Gunm, where a character desperately needs to call out to another but due to complicated circumstances can't say her name. So what does she say? A "Where are you?" or "Can you hear me?" would have done nicely. But instead she says nothing as a substitute for Say My Name.
In Hana Kimi, a remembered sex scene features Nanba and Kanako yelling each others names, which apparently turns them on.
This trope is parodied in episode 19 when the girls from Lobelia academy force Haruhi to be in their play, where she is cast as the helpless maiden opposite Benio as the male protagonist. Her only line is "Frederick-sama" which she says over and over in the same monotone voice.
Getter Robo Armageddon has two awesome moments coming from Go:
Go: [after being released] CHAAANGE! SHIIIN DRAAAGOOON!
Go: [after realizing who the pilot of Black Getter is] RYYYOOOUUUMAAA!
Weaponized at the climax of Persona 4: As Yu is being absorbed into Ameno-Sagiri, the entire Investigation Team calls out to him, simultaneously evolving their Personas into their ultimate form. SEMPAAAIII!/YU-SEMPAAAI!/YUUU!/NARUKAMIII!
Weiss Kreuz gives us Aya running down halls waving a sword over his head, screaming "TAAAKAAATOOORIII!"
Kasei Yakyoku: "TAKAAA!", from Sara when the Great Kanto Earthquake is unleashed
Oniisama e...: One of Nanako's trademarks is her screaming "Saint-Juste-sama... Saint-Juste-sama... SAINT-JUSTE-SAMAAA!"
Gankutsuou: Franz is guaranteed to scream "ALBEEERRRT!" whenever his best friend is in trouble. Albert himself has a habit of yelling "Count!" ("Hakushaku!"). This is a fairly good indicator of the show's relationshipdynamics.
Interestingly and heartbreakingply played with in the manga version of X/1999. When Artificial Human Nataku meets Karen Kasumi, he tells her his backstory — including how he was cloned from a dead Ill Girl named Kazuki. When Nataku dies via Taking the Bullet for Karen's sake, Karen doesn't scream "NATAKU", but she instead calls out for "KAZUKIIII"
And of course, the three related media (the manga, The Movie and the TV series) indulges massively in this: "KOTORIIII", "KAMUIIIII", "FUUUMAAAAAAA!"
Kotori in Yu Gi Oh ZEXAL. Her only role in the entire show is to support Yuma by saying his name nine bajillion times per episode. She serves very little purpose other than this.
Joseph Joestar lets out one of these in JoJo's Bizarre Adventure when he finally realizes that his friend, Caesar Zeppeli, is dead.
Blood-C has a lot of characters saying Saya's name, particularly Tadayoshi. Then, in the movie, you got Saya screaming, "FUMITOOO!" who is the Big Bad.
There's a joke where Germany will yell Italy's name in exasperation because of his obvious uselessness.
Estonia will scream Latvia's name in horror whenever this is used as a The Chew Toy by Russia, this is frequent enough as to be considered his Catch Phrase
Kill la Kill has Ryuko and Satsuki, who often indulge in this while fighting, with the traditional screaming. Outside of that, they tend to play a sort of Marco Polo; whenever one says the other's full name, the other says the name of the first in as disdainful and venomous a tone they can muster.
Utilized hilariously in Angel Beats!, during a Dwindling Party sequence where the characters are being killed off one-by-one; each time a character is killed off, everybody screams the character's name... until it gets to Naoi: