If you want a name that directly refers to the mechanic, something like "Typepool" could work if it doesn't sound too weird.
Anyway, it seems fun, will you use restrictions or only bans? As in Shell Smash can't be used by Iron Bundle but Cloyster can still use it.
And if this works like STABmons, that means every mono typed Pokémon get access to every move naturally learned by Arceus and Arceus gets every move naturally learned by mono typed Pokémon, right?
Tauros (Kanto) seems like it could be really good once it gets released, gaining Maushold's signature moves, all of Arceus moves, and powerful abilities like Guts, Quick Feet, Stakeout and Technician.
Another tier with Boomburst Sylveon is always welcome. All the eeveelutions seem great, they get pretty much every coverage move they could wish for, the abilities already mentioned for Tauros on top of some stuff they get from their own types, like Jolteon gets Electric Surge, Espeon gets Speed Boost, Leafeon gets Poison Heal, Vaporeon gets Unaware and Regenerator, Flareon gets Drought. Other stuff they all get includes Intimidate, Tidy Up, Roost, U-Turn, Rapid Spin, Nasty Plot, Swords Dance and Belly Drum.
Rotom-Fan may actually be good here, it gets Quiver Dance, Volt Absorb, Roost, Taunt and Hurricane, but not much coverage other than Icy Wind.
Copperajah seems quite strong, gaining Steely Spirit, Close Combat, SD and a lot of other great moves like Shed Tail, kind of want Melmetal to come back to do it better (and Kinklang to add Shift Gear).
The semi-official mascot gets access to Quiver Dance, Eruption, Drought and Earth Power thanks to Oricorio and Torkoal, it may not be just a meme.
Ape gains No Retreat and Guts, may even more stuff if it can get stuff from Arceus-Fighting once it becomes legal, Recover would be a very big deal.
The Fairy/Psychic get to share Teleport, Stealth Rock, Nuzzle and Magic Bounce, turning them into premier support Pokémon.
Gyarados get a lot of stuff from Magikarp, including Jet Punch, Wave Crash, Regenerator, Close Combat and Adaptability, and then it gets even more stuff from Pelipper like Drizzle, Knock Off, Roost, Brave Bird and U-Turn.