Since there isn't an organized list of all the Pokémon characters, I decided to make one.
Unapproved Pokémon-Owner
Kantian the Drowzee-JG87NL
Ghost the Shuppet-litwick222
Wrena the Umbreon-Wrena Kerdok
Slip the Mienfoo-pokeboy6
Danny the Oshawott-gerald1012
James the Chimchar-Pokejeenios
Blitz the Flareon-Wildfire
Darkblade the Deino-Deino Shadowdragon
Shawn the Zorua-Maxiorc
Silvia the Murkrow-Blu-Bird
Approved Pokémon-Owner
Kato the Pikachu-WarriorNick
Douglas the Sandshrew-Madcap
Monty the Spiritomb-Kentelekid
Galai the Ralts-Allamata
Myra the Snorunt-Raden
Mirage the Zorua-✰ShinyEevee✰
Ruby The Zangoose-Cutter Kirby
Skylar the Eevee-32Melody
Ilia the Kangaskhan-PS3rpchick
Kelsey the Ralts-I <3 Kirlia
Zera the Houndour-TatsuoKaneko
Rusty the Poochyena-Blasty
Rain the Mienfoo-NuzlockeNina
Cookie the Skitty-Orivexes
Zeri the Pawniard-ZeriqHaruk
Ivy the Eevee-Pocky
Vesper the Zorua-RikaScream
Lax the Munchlax-MunchlaxTime!
Clover the Shinx-Chocollie
Whimsy the Wooper-Whimsy
Seth the Tympole-DrakeX
Aaron the Aron-Smolt
Naomi the Eevee-NijiNeko
Battler the Duskull-ShadowDuskull
Rupin the Mudkip-themanofpokemon
Mimic the Ditto-LightHearted
Alex the Ralts-9kirby99
Sylvia the Chingling-HorseFeathers
Oliver the Cubone-Silverwing Bloodsplash
George the Buizel-MexterInfinite
Acro the Archen-bluekat12
Aislinn the Vulpix-LittleZombie
Mordred the Scraggy-Nocive
Teru the Oshawott-Teru
Winters the Snover-pokepal66
Aero the Archen-R-K-9
Newton the Abra-Altaeon
Isaac the Riolu-DarthKain
Dreydl the Riolu-LogicTest
Zilo the Tyrouge-Zilo
Sam the Buizel-Smashfan56
Vanity the Budew-DrakeTwi
Marek the Scyther-Theta_Rex
Maximus the Growlithe-Magpie (Original: pichugonnaeatchu)
Primrose the Plusle-Glaceon101
Astrid the Dratini-SereneLittleRose (Original: Broken Shadow)
Nocturna the Absol-Sakura (Original: LunaWolfen)
Radon the Riolu-Drawr (Original: Ignis)
Callie the Skitty-Twdtsquid (Original: Masquerade)
Bait the Carvanha-antonm1107 (Original: brushfire)
Flint the Poochyena-Drawr
Fermata the Mareep-HeadphoneGuru
Tallulah the Buizel-Headphone Actor
Ever the Oshawott-Sakura
Borein the Gligar-Tragar
Toxin the Poochyena-Magpie
Luna the Poochyena-TheShinyMew
Lilly the Lillipup-bangbronze
Volcanic the Charmander-Carmana
Claria the Emolga-Tdwtsquid
Treble the Sneasel-BaronVonAllen
Adorable the Snivy-pokefan99
Sleepy the Cubone-xXSleepyXx
Ace the Snivy-Epic Kirby
Rao the Purrloin-BlueLove
Abira the Bagon-Starsuri
Jake the Tepig-sdds1234
Jeff the Charmander-JeffMandM
Re the Treeko-SilverScale
Legretta the Snivy-IAmTheLeaf
Davonta the Pikachu-Davonta
William the Gastly-Savato
Div'et the Sandshrew-Wistuffly
Sofie the Mareep-Cherry
Stryke the Scyther-Shadowscyther
Tom the Totodile-antonm1107
Starfire the Vulpix-Tenshineko
Nate the Pikachu-Pikashock
Shaman the Riolu-zashonfire
Isa the Oshawott-Flamewolf
Michael Heat the Charmander-thekyle96
Enzu the Pawniard-Axineld
Keyami the Meowth-Ripple
Izumi the Shiny Absol-FoxFireAlchemist
Tsukishiro the Absol-SereneLittleRose
Spark the Electrike-AceofSpades
Laura the Shinx-Hero
Rena the Pichu-RAVE
Helia the Larvesta-Likablerouge
Mellow the Oddish-PandaWarrior101
Jacky the Starly-riolu77
Cobalt the Nincada-Duskerno
Ren the Torchic-Ren Shimizu
Starr the Shinx-star-bursts
Archived Pokémon-Original Owner
Arainia the Togepi-margeret44
Gensou the Zorua-Kataiyo
Ken the Oshawott-Water Blade
Searn the Charmander-Special Operative Blaire
Axrion the Axew-Super-Moose-Caboose
Akuroma the Ralts-Akuroma
Altair the Gilgar-Aerosmith71
Marley the Munchlax-MattL1222
Ho 'Ailona the Seel-Mamading
Lincoln the Riolu-whitewash
Venus the Mawile-NovaBox
Nicole the Emolga-cynda1
Kol the Meditite-Wolfgang
Fang the Gible-TunnelFang
Azul the Swablu-SapphireLucario100
Ally the Axew-Waterlily101
Kira the Riolu-Dawncloud1224
Vorona the Murkrow-MephistoFiesta
Nova the Shinx-Flashflood
Number of Pokémon claimed-#-Status
Larvesta-1-Unique
Pichu-1-Unique
Shinx-3-Average
Drowzee-1-Unique
Shuppet-1-Unique
Umbreon-1-Unique
Meinfoo-2-Unique
Oshawott-5-Common
Chimchar-1-Unique
Flareon-1-Unique
Deino-1-Unique
Pikachu-3-Average
Swablu-1-Unique
Sandshrew-2-Unique
Spiritomb-1-Unique
Ralts-4-Average
Snorunt-1-Unique
Zorua-4-Average
Zangoose-1-Unique
Eevee-3-Average
Kangaskahn-1-Unique
Houudour-1-Unique
Poochyena-4-Average
Skitty-2-Unique
Pawniard-2-Unique
Munchlax-2-Unique
Axew-2-Unique
Wooper-1-Unique
Tympole-1-Unique
Aron-1-Unique
Duskull-1-Unique
Mudkip-1-Unique
Ditto-1-Unique
Chingling-1-Unique
Cubone-2-Unique
Buizel-3-Average
Archen-2-Unique
Vulpix-2-Unique
Scraggy-1-Unique
Snover-1-Unique
Riolu-6-Banned
Abra-1-Unique
Murkrow-2-Unique
Tyrouge-1-Unique
Budew-1-Unique
Scyther-2-Unique
Growlithe-1-Unique
Plusle-1-Unique
Dratini-1-Unique
Togepi-1-Unique
Charmander-4-Average
Gligar-1-Unique
Seel-1-Unique
Mawile-1-Unique
Emolga-2-Unique
Meditite-1-Unique
Gible-1-Unique
Absol-3-Average
Carvanha-1-Unique
Mareep-2-Unique
Lillipup-1-Unique
Sneasel-1-Unique
Snivy-3-Average
Purrloin-1-Unique
Bagon-1-Unique
Tepig-1-Unique
Treeko-1-Unique
Gastly-1-Unique
Totodile-1-Unique
Meowth-1-Unique
Oddish-1-Unique
Starly-1-Unique
Nincada-1-Unique
Torchic-1-Unique
Electrike-1-Unique
Shinies-1-Unique
NOTE: Any Pokémon missing from the list might have changed folders or created after I edited the list. I will get them in the future.