Here’s all the aliases I’ve found in Pokédex entries (and the games they’re first mentioned in):
Alolan Raichu: hodad (Ultra Sun)
Alolan Vulpix: Keokeo (Sun)
Electrode: The Bomb Ball (FireRed)
Exeggutor: The Walking Tropical Rainforest (FireRed), The Walking Jungle (Diamond/Pearl)
Hitmonlee: the kicking master (Stadium), the Kick Master (Crystal)
Chansey: doctors' doubles (Legends: Arceus)
Goldeen: the Water Queen (Red/Blue), the water dancer (Stadium), princess of the water (Ultra Moon)
Starmie: the gem of the sea (Ruby)
Scyther: a ninja (Ultra Moon)
Jynx: the Queen of Ice (Sword)
Gyarados: the deity of destruction (Ultra Sun)
Moltres: the legendary bird of fire (Red/Blue), the fire bird (Stadium)
Dratini: the Mirage Pokémon (Diamond/Pearl)
Dragonair: the divine Pokémon (Crystal)
Dragonite: sea guardian (Stadium), the Sea Incarnate (Ultra Sun)
Noctowl: the emperor of dark nights (Ultra Sun)
Lanturn: The Deep-Sea Star (Ruby)
Slowking: the sage of the sea (Ultra Moon)
Remoraid: sniper of the seas (Ultra Moon)
Shiftry: the guardian of forests (Emerald)
Sharpedo: the Bully of the Sea (Ruby), the the vicious and sly gangster of the sea (Emerald), ruffian of the seas (FireRed/LeafGreen), the bandit of the seas (HeartGold/SoulSilver)
Absol: the disaster Pokémon (Ruby)
Flygon: the elemental spirit of the desert (Ruby), the Desert Spirit (Diamond/Pearl)
Mega Salamence: the blood-soaked crescent (Moon)
Chimchar: Lantern-Tail (Legends: Arceus)
Empoleon: Master of the Waves (Legends: Arceus)
Honchkrow: Summoner of Night (Platinum)
Drifloon: the Signpost for Wandering Spirits (Platinum)
Drapion: the Sand Demon (Shield)
Finneon: Beautifly of the Sea (Pearl), finery fish (Legends: Arceus)
Abomasnow: the abominable snowman (Diamond), The Ice Monster (Pearl)
Uxie: The Being of Knowledge (Diamond)
Mesprit: The Being of Emotion (Diamond)
Azelf: The Being of Willpower (Diamond)
Excadrill: the Drill King (Shield)
Basculin: the thug of the lake (Blue-Striped, Ultra Moon)
Sandile: the cleaner of the desert (Ultra Moon)
Krookodile: the Bully of the Sands (Sword)
Gothorita: the Witch of Punishment (Sword)
Beartic: the Snow-White Demon (Violet)
Braviary: the hero of the sky (Sun)
Larvesta: the Larva That Stole the Sun (Scarlet)
Volcarona: the rage of the sun (Ultra Sun)
Landorus: The Guardian of the Fields (Black)
Primarina: songstress (Ultra Moon)
Wishiwashi (School Form): demon of the sea (Ultra Sun/Ultra Moon)
Palossand: The Beach Nightmare (Sword)
Tapu Koko: guardian deity of Melemele (Sun)
Tapu Lele: guardian deity of Akala (Sun)
Tapu Bulu: guardian deity of Ula’ula (Moon)
Tapu Fini: guardian deity of Poni (Moon)
Cosmog: the child of the stars (Moon)
Cosmoem: the cocoon of the stars (Ultra Sun)
Solgaleo: the Beast That Devours the Sun (Ultra Moon)
Lunala: the Beast That Calls the Moon (Ultra Sun)
Hatterene: the Forest Witch (Shield)
Gigantamax Hatterene: the Raging Goddess (Shield)
Zacian (Crowned Sword): the Fairy King’s Sword (Shield)
Zamazenta (Crowned Shield): the Fighting Master’s Shield (Sword)
Gigantamax Single Strike Urshifu: the embodiment of rage (Sword)
Overqwil: sea fiend (Legends: Arceus)
Koraidon: Winged King (Scarlet/Violet)
Miraidon: Iron Serpent (Scarlet/Violet)
There are also a few official aliases that don’t appear in dex entries:
Dialga: almighty/great Sinnoh (according to the Diamond Clan)
Palkia: almighty/great Sinnoh (according to the Pearl Clan)
Giritina: the banished Pokémon, Arceus’s shadow
Manaphy: Prince of the Sea
Arceus: The Original One, almighty/great Sinnoh
Mega Diancie: the Royal Pink Princess
Oranguru (collectively): the people of the forests
Type: Null: Beast Killer, Type: Full
Nihilego: UB-01 Symbiont
Buzzwole: UB-02 Absorption
Pheromosa: UB-02 Beauty
Xurkitree: UB-03 Lightning
Celesteela: UB-04 Blaster
Kartana: UB-04 Blade
Guzzlord: UB-05 Glutton
Ultra Necrozma: the Blinding One
Poipole: UB Adhesive
Stakataka: UB Assembly
Blacephalon: UB Burst
Calyrex: the King of Bountiful Harvests (correct me if I’m wrong on this one, I haven’t played CT yet)
This might not be all of the aliases. I’d have to check every Pokédex entry to find them all. If I find any more, I’ll add them to this answer.
