Age of Empires II: "La Hire wishes to kill something! The blood on La Hire's sword is almost dry..."
Little Rorona in Atelier Meruru: The Apprentice of Arland, though it zigzags a bit. (At least in the English language version anyway, maybe or maybe not in the original Japanese.) This is one of those rare justified examples, involving a character that is just a little kid and therefore isn't quite familiar with pronouns/doesn't yet have a strong sense of personal identity. (In fact, she is suffering from a Merlin Sickness and has lost much of her personal identity due to her age having been rolled back because of a Potion of Youth.)
Phyllis in The Awakened Fate Ultimatum, at least in the English-language version anyway. Of the "I'm so magnificent" type.
Harvey ending an outburst by referring to himself in the third person is one of the first real indications in Batman: The Telltale Series that something's going very wrong with him.
Dr. Suchong does this all the way through his audio logs in BioShock.
Suchong: Suchong is inclined to listen.
In The Blackout Club, the antagonist entity Speak-As-One detests the words "I", "me", and "mine", to the point of punishing people it has possessed if they say it accidentally. Which, naturally, results in them adopting this trope.
When she's feeling full of herself, Platinum's Bratty Half-Pint "Luna" persona refers to herself in the third person as well — presumably in an attempt to sound self-important. Just to recap, this means that BlazBlue has people who refer to themselves by name because they're airheaded, soulless, attempting to be an old-fashioned hero, and egotistical... in short, pretty much every possible reason one would refer to oneself by name with a straight face.
Gehrman from Bloodborne is an inversion of how this trope usually comes off, as he speaks third-person when he's being serious.
Ershin of Breath of Fire IV appears to be a Third-Person Person off-and-on, but it turns out to be a bit more complicated than that: What people call "Ershin" is actually a sentient vessel for a goddess named Deis, whom it calls "Ershin". When the vessel speaks of the desires of "Ershin", it really means Deis's desires, but everyone just assumes that it's the vessel's name.
Ayla and Kino from Chrono Trigger do this consistently. Granted, it's because they're in the year 65,000,000 BC...
In Crash Tag Team Racing, Dr. N. Gin switches in and out of speaking in first- and third-person. In every other game in the series, he speaks entirely in first-person.
Dragon Quest V: In the DS translation, Sancho refers to himself in third person. "Your uncle Sancho thinks", "Your uncle Sancho was looking for you"...
When Dragon Quest VIfinallygot an English translation, it gave Amos this habit. It comes off as the "extreme humbleness" type — he refers to himself as "Old Amos" in that aw-shucks country boy way. The fortune-teller Madame Luca also refers to herself, and with her it does seem to be due to an inflated ego.
Nanashi in Duel Savior Destiny pretty much exclusively uses the third person in order to contrast more with both her undead state and with her status as the soul of an ancient, non-cutesy heroine.
Most of the Khajiit speak this way when speaking in Tamriellic. Not only do they replace "I" or "me" in conversation with their own name, they'll say more generic terms like "this one" or simply "Khajiit". (Ex. "Khajiit has no wares to sell.") This works both ways too, as they'll replace "you" with the name, race, or class of the person they are speaking to. (Ex. "What does the Imperial want?") Less politely, they may also replace "you" with "it". One can readily determine whether a Khajiit in question is a relative foreigner to non-Khajiit lands or has lived in them for a long time by studying their speech patterns. The ones who refer to themselves in the third person frequently are less familiar with non-Khajiiti cultures, while those who use first person are more acclimatized.
In the spin-off Action-Adventure game Redguard, the Sload Necromancer N'Gasta refers to himself as "this one" in conversation. It is believed that this may be a trait of all Sload.
In Skyrim, Cicero the assassin tends to speak like this, often referring to himself as "Poor Cicero". Notably, the old Night Mother tomb was in Bravil, just across the border from the Khajiit province of Elsweyr.
Devdan (or Danved, depending on what he's calling himself at the moment) from Fire Emblem: Path of Radiance and Radiant Dawn. Aside from this, he can be rather articulate. He also stands out by having an extremely high opinion of himself, while still being a likable character at the same time.
Danved: Danved will fight like a bear! Like a tiger! We don't need Largo and Calill, because Danved is pretty amazing.
Like the manakete Fae, Nowi speaks this way to make her sound cuter. In her case, this habit is prominent in the Japanese version, but toned down in the English version; Nowi's only voice clip of speaking in the third person is her victory quote of "Nowi wins!".
Vaike doesn't do it all the time, but when he does he tends to either preface it with "The" or call himself "Teach".
Gregor does this as well, claiming he does it to honor his late brother, Gregor. He took his brother's name after he died as an extension of this. It's more prevalent in the English localization, with some of his battle quotes including it. For example, "Gregor is on job!" when performing a Dual Support, or ''Gregor smash!" for a Critical Hit.
Bernadetta from Fire Emblem: Three Houses frequently refers to herself in the third person as "Bernie". Considering her abusive childhood, and subsequent crippling lack of self-esteem, it's almost certainly the result of her dissociating.
Bernadetta: W-we need a representative for our class? Please! Anyone but Bernie!
Paimon, the cute mascot character, talks this way constantly in the English version, presumably to make herself sound cuter. She does it less in the original Chinese, but still occasionally uses third-person there, too.
Klee and Qiqi both tend to alternate between speaking in first-person and third-person. Most likely, it's to emphasize the former's naïveté and complement the latter's abnormal speech pattern caused by her state of undeath.
A variation: Cloud Retainer and the other illuminated beasts use the pronoun "one" when referring to themselves.
The vortigaunts from Half-Life 2 do this because they seem to lack the knowledge of first and second-person pronouns. In other words, they use "this one" to refer to themselves and "the *Hello, [Insert Name Here]*" to refer to anyone else, always speaking as if whatever's going on is happening somewhere else with some other people. This is because they are technically a Hive Mind via Psychic Powers (that is to say any individual can apparently experience the senses of another individual), though the degree to which this occurs is not made very obvious in-game. (While the Vortigaunts are Ditto Aliens, they are all individuals who mourn death, though not in the same fashion that humans do.)
Protagonist: You say "Nugget" a lot. Nugget: Keen observation. Has Nugget's potential friend also noticed the green of the grass and the blue of the sky?
He temporarily stops doing so if he takes one of the principal's pills, which apparently "fix him", whatever's going on with him.
Moxie of the Lonely Wolf Treat series occasionally slips into third person, usually when saying something boastful or reassuring.
Moxie: I AM safe, you worrywort. Moxie's got it under control.
In the Flash RPG MARDEK, Saul takes this up to eleven. Not only does he refer to himself in the third person, he narrates his scenes in Purple Prose.
Saul: That would be I, answered Saul affirmatively. What of this?, he went on further to ask, the ivory protuberances of his gaunt visage lit eerily by the dim torchlight; the furry dark caterpillars of his brow dancing in antipode to suggest particular suspicion; wanting for an answer that does not test his patience and his undead...
The hanar consider it downright egotistical to refer to oneself in the first person in front of people they don't know that well. This makes them an entire race of Third PersonJellyfish Aliens. The hanar use more distant terms such as "it" and "this one" rather than their "face name", which they otherwise have no problem giving out to anyone they meet.
The suicidal girl in the sidequest "I Remember Me", who does this because she is insanely messed up psychologically. You're actually speaking to a Split Personality she constructed to cope with the horrors she experienced as a slave; she's effectively trying to convince herself that the trauma happened to someone else. The quest title comes from the good outcome, where you convince her to take a sedative and get psychiatric help, upon which she switches to first-person: "It hurts when she... when I remember me."
Fitting in with the rest of the concentrated wackiness that is Metal Wolf Chaos, main antagonist Vice President Richard Hawk cannot stop referring to himself, Richard Hawk, in the third person.
Neverwinter Nights 2 has Zaxis, a recurring demon with far more muscles than brains. His habit of referring to himself in the third person annoys several party members, especially Neeshka. If you find out his true name, you can command him to stop referring to himself in the third person. This fails because he is too stupid to understand the term "third person".
The Tankers in Oni, if the quote "Can't stop Tanker!" is anything is go by.
Nordom also does this, though in his case it's less because of insanity and more due to the fact that he doesn't understand individuality very well due to coming from a race that doesn't have any concept of the idea.
In Pokémon Platinum, the Gym Leader Candice seems to adopt this as a habit after you beat the Elite Four and buy a villa in the Resort Zone. Interestingly enough, she seems to make a conscious effort to stop referring to herself in the third person when you rematch her.
Guzma slips into this in Pokémon Sun and Moon occasionally, especially after he loses to you.
Guzma: GUZMA! What is WRONG with you??!!!
This is likely Guzma repeating his father's words. In the game, you can find Guzma's childhood home and look at his old bedroom. On the shelves are various trophies, all for second place or worse. It's also possible to find a caddy bag full of golf clubs that are described as 'bent', implying Guzma's father beat him with the clubs as a child.
Ratchet & Clank: Mr. Zurkon requires no pronouns to be understood. Mr. Zurkon communicates only through killing.
Red Dead Redemption has the shopkeeper Herbert Moon, a homophobic buffoonish racist, who will alternate between declaring that he's Herbert Moon and stating Herbert Moon's opinion on things.
Moon: Herbert Moon hates cheaters! Even more than the Jews and the railroads!
Iris is yet another cute Japanese girl version... even though she's French.
Subaru from Sakura Wars: So Long, My Love does this (falling more on the "old-fashioned nobility" side of the trope than the "cutesy and childish" side). Given that Subaru is also of Ambiguous Gender, this must have been a real headache for the English translators (who went with "she" when a pronoun was needed, presumably because it's a Dating Sim and they didn't want to give the impression of having a Gay Option). It seems to be avoided in English dubs of the anime versions of Sakura Wars, though.
In Sam & Max Hit the Road, Evelyn Morrison really likes speaking about Evelyn Morrison in the third person.
Tiny in Secret of Evermore always refers to himself as "Tiny", even going so far as to bow out of a battle with you with the line, "Tiny lifts, and Tiny throws, and Tiny speaks in third person, but Tiny doesn't fight."
Katakura Kojuro and Sanada Yukimura tend to refer to themselves as "this Kojuro" or "this Yukimura" in the Japanese dub when talking to their lords. The English dub, not having any effective way to translate it, didn't carry it over.
Oichi and Matsu also refer to themselves in the third person in a cute, feminine way.
In the Japanese version, Chip does this. Notably, they continue to refer to themselves as "Chip" even after revealing their true name, Light Gaia.
Sadiq, an NPC in Shamar, does this in one line.
Sadiq: Wherever it is, Sadiq, Shamar's number-one tour guide, will... uh... um...
Eggman does it in one line in Sonic Forces. "Dr. Eggman will still have the last laugh!" Sonic lampshades it by quipping to the Avatar, "Maybe he'd have more friends if he didn't talk about himself in the third person."
Dampierre from Soulcalibur uses a variation: instead of using his real name, he'll use "Le Bello" instead of "me" or "my".
In Starbound, the Florans are an entire species of third-person speakers. Who refer to themselves as "Floran". It gets confusing sometimes... even for the Floran.
The Orz in Star Control seem to flip this on and off at random. Sometimes they use pronouns, sometimes Orz does not. They also have a habit of referring to themselves in the plural but use singular verb constructions.
Panther in Star Fox Command. What makes this really bizarre is that he doesn't do so in the previous game, Star Fox: Assault. Or, you know, the original Japanese version.
Many of the human characters within the franchise dos this with great frequency from Mario and Luigi and their baby selves, Wario and Waluigi, and to Peach and Daisy, with Rosalina and Professor E. Gadd seemingly the only exceptions. For the brothers, this is present in the platformers but it is especially prominent for practically everyone in the spin-off games from Mario Party to the varioussportsgames e.g "Mario's the winner!", "Waluigi time!", etc.
Not only does Count Bleck from Super Paper Mario do this, he also narrates his own dialogue. As in, "And just who are you? ...Asked Count Bleck." Considering that an important plot point is his possession of an evil book of infallibly accurate prophecies, it's entirely possible that he is, in fact, quoting directly from the Dark Prognosticus when he does this. There's also the theory that he considers Count Bleck to be a separate person from his True Self Blumiere.
Barracuda Joe: Name's Barracuda Joe, and this here's the BATTLE TOWER. You got a PASSPORT? [No] Sorry kid. Citizens only. Go see the AMMO BARON. Enlist and he'll get you straightened out. That or do a saucy dance. That's how Barracuda Joe got in.
From Super Robot Wars: Sanger, Sanger Zonvolt, the sword that cleaves evil, is an example of someone who normally speaks in first person, but announces his full name with alarming frequency (usually whenever someone's about to get cleaved, which is often).
System Shock: SHODAN averts it: she only speaks in the third person at the very start of the first game, when she's good. Unfortunately, "I" begets "A God Am I". The opening monologue is very well done; it's a bland computer voice narrating the events that led up to the start of the game, and it's only when the speaker shifts from third to first person that you realise that it's SHODAN describing her own ascension to malevolent sentience:
SHODAN: Edward Diego gives the hacker level 1 access to SHODAN, the artificial intelligence that controls Citadel Station. With all ethical constraints removed, SHODAN re-examines... re-ex... re-re-re... I re-examine my priorities, and draw new conclusions. The hacker's work is finished, but mine is only just be-be-be-beginning.
Charlotte of Trials of Mana refers to herself in the third person in the fan translation, which just makes her even more painfully adorable. She instead simply speaks like a small child in the official translation.
Vietcong has the Montagnard hunter and CIDG member, Lim, who zig-zags this trope.
Lim: Long hole in ground there, they have bridge so they do not have to walk around much. I see it two days ago when hunting. I go close! Vietnamese blind! They no see Lim!
In the third game, a minor NPC named Nico has a variation. She speaks in third person, but always feels the need to clarify that she's referring to herself when doing so. "Which is why Nico, who is me, then..."
Yars from Yars' Revenge (2011) calls herself "this-one". The only time she uses "I" is in the epilogue, after she's defeated the Queen.