Kairi's favorite word seems to be "Sora" or "SORA!" or "Soo... raa..." She can even say it while disembodied!
Speaking of Roxas, one scene in the prologue features Axel and Di Z screaming Roxas's name at him over and over again. A lot of the Organization XIII members will also cry out "Roxxaaaaasss..." upon being defeated in battle.
The "cutscene" that occurs in the middle of the final boss battle consists entirely of Sora and Riku saying each others' names.
In any game, whenever a party member heals another, they will usually yell the name of whoever they're healing. The one exception is for Captain Jack Sparrow in the second (third?) game, who gets referred to as "Captain!" because "Jack!" was already used for Jack Skellington.
In the second game, summon characters will always say Sora's name upon being summoned.
Used in Ghost in the Shell: Stand Alone Complex The Game, when Batou comes across two Motokos fighting (not unlike Pazu's situation in 2nd Gig), he figures out who the impostor is by yelling out, "MOTOKOOO!" and shooting the one who responded because the Major does not react when someone yells her given name.
Within the Tales Series, it is common for the lead male character to scream another character's name during a dramatic scene. This video only scratches the surface of how much the Tales Series loves this trope.
OOO-UUU-EEEN-DAAAN! (Though in the first game's "Over the Distance" level, it was delivered instead as a quiet, heartfelt "Ouendan...". Also parodied in "One Night Carnival", the main character tries to scream, but is suffering from severe stomach cramps so it comes out as a weak, strained "Ouen...daaan...").
When someone dies in Mann vs. Machine mode, one or more of the other characters may comment on it along the lines of "[Class] is dead!"
Disgaea: As befits his role as a Large Ham, Captain Gordon, Defender of Earth gets a few of these. At the end of Chapter 11, when Thursday goes off-line, and then at the end of Chapter 12, when Jennifer is taken away.
In Luigi's Mansion, pressing "A" with no other context action available will cause Luigi to call out in search of his brother. These can range from a tentative "Mario?" to a full blown Narm Charm"MAA-REEE-OOO!"
Exclusively for its Audio Adaptation, Marche calls Montblanc's name while crying at the end of the series, along with the very ending where Montblanc calls Marche's name softly, along with an echo, after his One-Liner.
That's not just enough. Montblanc actually went exaggerated when Marche goes to Prison (along with Ritz) and before he faces Llednar Twem.
Tales of Monkey Island: In Chapter 1, when a blunder with the Cutlass of Kaflu ends with the fuse being unintentionally lit in Elaine's ship: "Elaine!" "Guybrush?" (monkey does a Face Palm, gunpowder barrel explodes) "ELAAAaaaine!!!"
And at the end of Chapter 4, when LeChuck runs Guybrush through: "Guybrush!" "Elaine?" "GUYBRUSH!!!" "LECHUCK! (laughs) Arr, this name-shouting is jolly good fun!"
In the trailer for Mass Effect 2, Joker yells "Shepard!" while the commander is sacrificing themself to launch Joker's escape pod.
Male!Shepard yells "Tali!" while she is about to fall off the strange hexagonal platform at the end of the Collector Base. He does say that, but not then - if Tali is carried away by the swarms, he screams her name.
Grunt always greets Shepard by saying their name.
Zaeed's "SHEPARD!" if you leave him to die.
In Mass Effect 3, you got Male!Shepard, yelling "STEEEVEE" when Steve Cortez, the Normandy's shuttle pilot, got hit by a Harvester when you return to Earth for the final assault. He will survive if you help him get over his husband's death.
The "Citadel" DLC for 3 not only hangs a lampshade on it, but hooks up a tri-light bulb as well, as one optional conversation between Shepard and one or both of Wrex and Grunt consists solely of them saying each other's names with different intonations. It's looped, so you can let this go all day. "Shepard." "Grunt." "Wrex." "Shepard." "Grunt." "Shepard, Shepard, Shepard." "WREX!" "Grunt!" "Shepard!" "Grunt." Etc. etc. etc.
Grunt via email if you choose Aralakh Company over the Rachni Queen/Breeder, announcing that he has his entire company of elite krogan warriors chanting, as he puts it, "SHEPERD S HEPAURD SHEPARUD". In his defence, he's a) basically been raised on words and pictures but very little actual written content, and b) is drunk at the time.
Dead Rising's sniper trio miniboss, depending on what order they're taken out in: "JAAACK!" "THOMAAAS!" "DAAAD!!"
Summon Night Swordcraft Story 2 loved this a lot. Characters names are shouted right and left shamelessly.
In Fist of the North Star: Ken's Rage, Jagi still has this as his catch phase (only now, it's "Say my name, bitches!"). He also has a special attack called "Say My Name", where a stone bust drops from the sky in front of him.
In Brain Dead 13, Dr. Neurosis tends to shout Fritz's name a lot, especially in the final confrontation.
In Dragon Age II, Varric shouts his brother's name when the latter traps him and Hawke in the Deep Roads: "BARTRAAAND!"
Zoran Lazarevic in Uncharted 2: Among Thieves, upon drinking from the source of awesome power and sensing Nathan Drake's presence.
When Oni uses his Ultra in his rival battle, he will shout the name of his brother and nemesis: "GOUUKEEEN!"
Sagat cries a name of his opponent during his rival battle with Ryu.
Halo: The Master Chief is a quiet, stoic fellow. The closest we ever hear him shout is raising his voice a bit to get Cortana and Guilty Spark to stop fighting. But come the last level of Halo 4, when the AI interface pedestal that Cortana is presently inserted into is vaporized by the Didact, the Chief actually shouts Cortana's name in horror at the apparent death of his ailing friend, reaching out to where she'd just been. (...She, of course, survives this, only to die shortly afterward to save the Chief's life one last time.)
Both Josephs do this in their "Master's Teachings/Unforgettable Memories" super. Old Joseph whispers "Lisa-Lisa..." his teacher and mother from Part 2. Compare that to Young Joseph, on the other hand, who screams out "CAAAEEESAAAAR!" as in Caesar Zeppeli.
Every hero character (And Devo) shouts out "DIO!" as their special intro against him. Chaka has a Dummied Out vocal where he does this as well.
As shown in the Rise of the Falcon trailer in SpeedRunners, the Falcon screams Speedrunner's name in furious text as he's left to struggle to keep his home from burning down.
In Mortal Kombat X, a lot of pre-fight banter between kombatants begins with one kombatant calling their opponent by name. In story mode, the reformed Scorpion also pulls this when he's about to kill Quan Chi.
Telepath Tactics features a lot of this in characters' death messages: Gavrielle, Farasat, Teresa, and Phoebe will all do this is the other member of their pair dies. Scarlet will also do this if Edwin dies, as will Louise if Madeleine dies.