Moves, that can't be taught through TM, even though the Pokemon should be able to learn the move. (Checked through Pokemon Showdown)

Hone Claws: Alolan Sandshrew/Sandslash, Mimikyu, Zeraora

Telekinesis: Alolan Raichu, Cutiefly, Ribombee, Comfey, Oranguru, Minior, Mimikyu, Bruxish, Dhelmise, Tapu Koko/Lele/Bulu/Fini, Lunala, Nihilego, Necrozma (all formes), Stakataka

Dig: Alolan Raichu, Alolan Diglett/Dugtrio, Alolan Marowak, Grubbin, Charjabug, Vikavolt

Ally Switch: Alolan Raichu, Alolan Graveler/Golen, Alolan Marowak, etc.
https://bulbapedia.bulbagarden.net/wiki/Ally_Switch_(move) for a full list. There's way too many Pokemon. Currently, only 15 Pokemon can actually learn it through the TM.

Incinerate: Turtonator

Retaliate: Alolan Marowak

Flash: Alolan Raichu, Alolan Exeggutor, Morelull, Shiinotic

Struggle Bug: Cutiefly, Ribombee, Wimpod, Golisopod

Pluck: Rowlet, Dartrix, Decidueye, Pikipek, Trumbeak, Toucannon, Oricorio (all forms)

Rock Smash: Alolan Raichu, Alolan Marowak, Pikipek, Trumbeak, Toucannon, Crabrawler, Crabominable, Passimian, Golisopod

Mega Punch: Alolan Raichu, Alolan Marowak, Buzzwole

Razor Wind: Type: Null, Silvally, Drampa

Whirlwind: Tapu Bulu

Mega Kick: Alolan Raichu, Alolan Marowak, Mudbray, Mudsdale, Stufful, Bewear

Body Slam: Alolan Raichu, Alolan Marowak, Litten, Torracat, Incineroar, Mudbray, Mudsdale, Turtonator

Take Down: Alolan Raichu, Alolan Exeggutor, Alolan Marowak, Yungoos, Gumshoos, Wishiwashi, Stufful, Bewear, Passimian, Type: Null, Silvally, Minior, Stakataka

Double-Edge: Alolan Rattata/Raticate, Alolan Raichu, Alolan Geodude/Graveler/Golem, Alolan Exeggutor, Alolan Marowak, Wishiwashi, Stufful, Bewear, Passimian, Type: Null, Silvally, Minior, Celesteela, Stakataka

Bubblebeam: Alolan Marowak, Popplio, Brionne, Primarina, Crabrawler, Crabominable, Dewpider, Araquanid

Water Gun: Alolan Marowak, Popplio, Brionne, Primarina, Wishiwashi, Bruxish, Tapu Fini

Pay Day: Alolan Raichu

Submission: Alolan Raichu, Alolan Marowak

Counter: Alolan Rattata/Raticate, Alolan Raichu, Alolan Sandshrew/Sandslash, Alolan Geodude/Graveler/Golem, Alolan Marowak, Lycanroc (Midnight and Dusk), Mudbray, Mudsdale, Pyukumuku, Jangmo-o/Hakamo-o/Kommo-o, Buzzwole, Marshadow

Seismic Toss: Alolan Raichu, Alolan Marowak, Passimian

Rage: Alolan Raichu, Alolan Exeggutor, Alolan Marowak, Type: Null, Silvally, Bruxish

Mega Drain: Alolan Exeggutor, Morelull/Shiinotic, Sandygast/Palossand, Dhelmise, Celesteela

Dragon Rage: Salandit/Salazzle, Drampa, Guzzlord

Fissure: Alolan Diglett/Dugtrio, Alolan Marowak

Teleport: Alolan Exeggutor, Cosmog, Cosmoem, Solgaleo, Lunala

Mimic: Alolan Raichu, Alolan Exeggutor, Alolan Marowak, Mimikyu

Bide: Alolan Raichu, Alolan Exeggutor, Alolan Marowak, Yungoos/Gumshoos, Mudbray/Mudsdale, Stufful/Bewear, Pyukumuku, Jangmo-o/Hakamo-o/Kommo-o, Stakataka

Self-Destruct: Alolan Geodude/Graveler/Golem, Alolan Exeggutor, Minior

Egg Bomb: Alolan Exeggutor

Swift: Alolan Raichu, Alolan Sandshrew/Sandslash, Alolan Persian, Minior, Pheromosa

Skull Bash: Alolan Raichu, Alolan Marowak, Tapu Bulu, Celesteela

Sky Attack: Rowlet/Dartrix/Decidueye, Pikipek/Trumbeak/Toucannon, Oricorio, Tapu Koko, Lunala, Naganadel

Psywave: Alolan Exeggutor, Bruxish, Tapu Lele, Nihilego

Tri Attack: Alolan Dugtrio, Type: Null, Silvally

Dynamic Punch: Alolan Raichu, Alolan Marowak, Crabrawler/Crabominable, Buzzwole

Headbutt: Alolan Raichu, Alolan Diglett/Dugtrio, Alolan Marowak, Jangmo-o/Hakamo-o/Kommo-o, Nihilego

Curse: Alolan Raichu, Alolan Sandshrew/Sandslash, Alolan Geodude/Graveler/Golem, Alolan Grimer/Muk, Alolan Exeggutor, Alolan Marowak, Rowlet/Dartrix/Decidueye, Sandygast/Palossand, Pyukumuku, Mimikyu

Rollout: Alolan Raichu, Alolan Geodude/Graveler/Golem, Alolan Exeggutor, Minior, Komala, Togedemaru

Zap Cannon: Alolan Raichu, Vikavolt, Xurkitree

Sweet Scent: Alolan Raichu, Alolan Exeggutor, Cutiefly/Ribombee, Fomantis/Lurantis, Salandit/Salazzle, Bounsweet/Steenee/Tsareena, Comfey, Tapu Lele

Snore: Alolan Rattata/Raticate, Alolan Raichu, Alolan Sandshrew/Sandslash, Alolan Vulpix/Ninetales, Alolan Diglett/Dugtrio, Alolan Meowth/Persian, Alolan Geodude/Graveler/Golem, Alolan Grimer/Muk, Alolan Exeggutor, Alolan Marowak, pretty much every Gen 7 Pokemon. for a full list: https://bulbapedia.bulbagarden.net/wiki/Snore_(move)

Icy Wind: Alolan Rattata/Raticate, Alolan Sandshrew/Sandslash, Alolan Vulpix/Ninetales, Alolan Meowth/Persian, Alolan Marowak, Popplio/Brionne/Primarina, Crabominable, Oricorio, Mareanie/Toxapex, Dewpider/Araquanid, Golisopod, Type: Null/Silvally, Drampa, Tapu Fini, Lunala, Pheromosa

Giga Drain: Alolan Grimer/Muk, Alolan Exeggutor, Rowlet/Dartrix/Decidueye, Dewpider/Araquanid, Fomantis/Lurantis, Morelull/Shiinotic, Bousweet/Steenee/Tsareena, Comfey, Sandygast/Palossand, Mimikyu, Dhelmise,  Tapu Bulu, Celesteela, Kartana

Endure: Alolan Raichu, Alolan Sandshrew/Sandslash, Alolan Diglett/Dugtrio, Alolan Geodude/Graveler/Golem, Alolan Exeggutor, Alolan Marowak, Grubbin/Charjabug/Vikavolt, Stufful/Bewear, Comfey, Pyukumuku, Turtonator, Buzzwole

Iron Tail: Alolan Rattata/Raticate, Alolan Raichu, Alolan Sandshrew/Sandslash, Alolan Vulpix/Ninetales, Alolan Meowth/Persian, Alolan Exeggutor, Alolan Marowak, Popplio/Brionne/Primarina, Yungoos/Gumshoos, Rockruff/Lycanroc (all forms), Wishiwashi, Salandit/Salazzle, Passimian, Turtonator, Togedemaru, Bruxish, Jangmo-o/Hakamo-o/Kommo-o, Solgaleo, Guzzlord, Poipole/Naganadel, Zeraora

Dragon Breath: Drampa, Jangmo-o/Hakamo-o/Kommo-o

Mud-Slap: Alolan Raichu, Alolan Diglett/Dugtrio, Alolan Marowak, Yungoos/Gumshoos, Grubbin/Charjabug/Vikavolt, Mudbray/Mudsdale

Ice Punch: Alolan Sandshrew/Sandslash, Alolan Grimer/Muk, Gumshoos, Crabrawler/Crabominable, Stufful/Bewear, Kommo-o, Tapu Fini, Buzzwole, Marshadow

Defense Curl: Alolan Raichu, Alolan Sandshrew/Sandslash, Alolan Geodude/Graveler/Golem, Minior, Komala, Togedemaru, Magearna

Thunder Punch: Alolan Raichu, Alolan Geodude/Graveler/Golem, Alolan Grimer/Muk, Alolan Marowak, Incineroar, Gumshoos, Crabrawler/Crabominable, Lycanroc (Midnight), Stufful/Bewear, Kommo-o, Tapu Koko, Buzzwole, Xurkitree, Marshadow, Zeraora

Detect: Alolan Raichu, Alolan Marowak, Kartana

Fire Punch: Alolan Geodude/Graveler/Golem, Alolan Grimer/Muk, Alolan Marowak, Incineroar, Gumshoos, Lycanroc (Midnight), Kommo-o, Marshadow, Zeraora

Fury Cutter: Alolan Sandshrew/Sandslash, Alolan Marowak, Fomantis/Lurantis, Golisopod, Kartana

Nightmare: Alolan Exeggutor

Focus Punch: Alolan Raichu, Alolan Sandshrew/Sandslash, Alolan Geodude/Graveler/Golem, Alolan Muk, Alolan Marowak, Incineroar, Crabrawler/Crabominable, Lycanroc (Midnight), Stufful/Bewear, Passimian, Kommo-o, Tapu Bulu, Buzzwole, Marshadow, Zeraora

Water Pulse: Alolan Meowth/Persian, Popplio/Brionne/Primarina, Wishiwashi, Mareanie/Toxapex, Dewpider/Araquanid, Golisopod, Bruxish, Drampa, Kommo-o, Tapu Fini

Bullet Seed: Alolan Exeggutor, Pikipek/Trumbeak/Toucannon

Shock Wave: Alolan Rattata/Raticate, Alolan Raichu, Alolan Meowth/Persian, Alolan Graveler/Golem, Alolan Grimer/Muk, Yungoos/Gumshoos, Grubbin/Charjabug/Vikavolt, Passimian, Turtonator, Togedemaru, Drampa, Kommo-o, Tapu Koko, Solgaleo, Lunala, Pheromosa, Xurkitree, Celesteela, Guzzlord, Necrozma (all forms), Magearna, Naganadel, Zeraora

Secret Power: Alolan Raichu, Alolan Vulpix/Ninetales, Alolan Exeggutor, Alolan Marowak,

Skill Swap: Alolan Exeggutor, Cutiefly/Ribombee, Sandygast/Palossand, Tapu Lele, Stakataka

Snatch: Alolan Rattata/Raticate, Alolan Meowth/Persian, Incineroar, Mareanie/Toxapex, Salandit/Salazzle, Oranguru, Passimian, Mimikyu, Bruxish, Pheromosa, Marshadow, Poipole/Naganadel, Zeraora

Brine: Wishiwashi, Tapu Fini

Dragon Pulse: Alolan Exeggutor, Salandit/Salazzle, Turtonator, Drampa, Jangmo-o/Hakamo-o/Kommo-o, Guzzlord, Necrozma (all forms), Poipole/Naganadel

Drain Punch: Incineroar, Crabrawler/Crabominable, Bewear, Passimian, Mimikyu, Hakamo-o/Kommo-o, Buzzwole, Guzzlord, Marshadow, Zeraora

Silver Wind: Cutiefly/Ribombee, Pheromosa

Recycle: Alolan Raichu, Alolan Muk, Morelull/Shiinotic, Sandygast/Palossand, Pyukumuku, Necrozma (all forms), Stakataka, Blacephalon

Avalanche: Crabominable

Stealth Rock: Alolan Sandshrew/Sandslash, Alolan Diglett/Dugtrio, Alolan Geodude/Graveler/Golem, Alolan Marowak, Rockruff/Lycanroc (all forms), Mudbray/Mudsdale, Sandygast/Palossand, Minior, Kommo-o, Nihilego, Necrozma (all forms), Stakataka

Captivate: Alolan Raichu, Alolan Vulpix/Ninetales, Alolan Meowth/Persian, Alolan Exeggutor, Alolan Marowak, Popplio/Brionne/Primarina, Oricorio, Salazzle, Steenee/Tsareena

Natural Gift: Alolan Raichu, Alolan Exeggutor, Alolan Marowak, Comfey, Drampa

Power-Up Punch: Alolan Grimer/Muk, Alolan Marowak, Crabrawler/Crabominable, Buzzwole

Cut: Kartana

Strength: Alolan Raichu, Alolan Exeggutor, Alolan Marowak

Defog: Torchic/Combusken/Blaziken, Seedot/Nuzleaf, Volbeat, Illumise, Swablu/Altaria, Castform, Chimecho, Rayquaza, Carnivine, Rotom, Snivy/Servine/Serperior, Pidove/Tranquill/Unfezant, Woobat/Swoobat, Cottonee/Whimsicott, Sigilyph, Ducklett/Swanna, Emolga, Cryogonal, Hydreigon, Volcarona, Tornadus, Thundurus, Reshiram, Zekrom, Landorus, Fletchling/Fletchinder/Talonflame, Vivillon, Florges, Hawlucha, Klefki, Noibat/Noivern, Xerneas, Yveltal, Volcanion, Rowlet/Dratrix/Decidueye, Pikipek/Trumbeak/Toucannon, Oricorio, Cutiefly/Ribombee, Fomantis/Lurantis, Comfey, Silvally, Drampa, Tapu Koko, Tapu Fini, Lunala, Kartana

Rock Climb: Alolan Geodude/Graveler/Golem, Rockruff/Lycanroc (all forms)

Whirlpool: Wishiwashi, Dhelmise, Tapu Fini

Dive: Wishiwashi