Cosplay Pikachu
In ORAS, there is an NPC that will gift the player Cosplay Pikachu. This Pikachu can switch costumes or remove the costume in any Contest Hall by talking to the Pokemon Breeder in the green room. When changing costumes, the Cosplay Pikachu will learn a move associated with the costume.
Source: https://bulbapedia.bulbagarden.net/wiki/Cosplay_Pikachu
Deoxys
In Gen III the forms were game specific. After Gen III, however, the forms were able to be changed by interacting with meteorites found throughout the games in the overworld, with SV introducing a Meteorite item to cycle through the forms.
Source: https://bulbapedia.bulbagarden.net/wiki/Deoxys_(Pokémon)#Form_data
Rotom
Like Deoxys, Rotom changes form by interacting with Rotom appliances in the overworld in games that let it change form and don't have the Rotom catalogue.
Source: https://bulbapedia.bulbagarden.net/wiki/Rotom_(Pokémon)#Form_data
Ash-Greninja
Greninja with Battle Bond transforms into Ash-Greninja after fainting an opponent. In SV however, Ash-Greninja form was removed and now only gives Atk, SpAtk, and Spd increase.
Source: Experience and https://bulbapedia.bulbagarden.net/wiki/Battle_Bond_(Ability)
Furfrou
In XY there is a shop that can trim Furfrou's fur for $500 called Friseur Furfrou. The trim lasts for 5 days or until the Furfrou is deposited into the PC.
Source: https://bulbapedia.bulbagarden.net/wiki/Vernal_Avenue#Friseur_Furfrou
Zenith Marshadow
From my understanding, it does not appear to be an actual form in the game, rather just a name given to its appearance when it does certain animations. When Marshadow turns green during animations, (or purple if it's shiny,) is when Marshadow is considered in it's "Zenith Mode."
Source: https://pokemondb.net/pokebase/410535/what-is-marshadows-zenith-form and https://bulbapedia.bulbagarden.net/wiki/Marshadow_(Pokémon)
Cramorant
Cramorant changes form thanks to its ability, Gulp Missile. When Cramorant uses Surf or Dive, it catches Arrowkuda in its mouth when over 50% HP (Gulping Form), or a Pikachu when under 50% HP (Gorging Form). When hit by an attack, Cramorant spits them out and returns to normal form.
Source: Experience and https://bulbapedia.bulbagarden.net/wiki/Gulp_Missile_(Ability)
Gimmighoul
In Pokemon SV, Chest form can be caught after interacting and battling them. When you interact with a Roaming form Gimmighoul, they give Gimmighoul Coins but run away. The Roaming Form can only be caught in Pokemon Go then transferred through Pokemon Home.
Source: Experience and https://bulbapedia.bulbagarden.net/wiki/Gimmighoul_(Pokémon)