In the Pokemon: Let's Go games, you could obtain Alolan forms of pokemon by trading with NPCs. Are there similar NPCs in Pokemon Sword and Shield, or some other way to obtain Alolan Pokemon?
Isle of Armor
In the Isle of Armor DLC, there is a mini-game in which you are tasked find Alolan Digletts throughout the island. By collecting these Diglett, you will be given various Alolan forms (as well as a Kantonian form and Alola starter) as rewards for returning them to their owner.
You cannot obtain Alolan forms in the base version of Sword and Shield, but you can by transferring Pokemon into the game via Pokémon Home (as long as the base form exists with in the Pokedex) or by trading with others players who transferred them from Pokemon Home
Alolan forms do existin the Galar region, as Alolan Meowth can be found in one of the camps. This camp is located on Route 7, and is known as “Renee’s Camp”
Alolan ninetails is coded into the game as a raid battle on the island’s peak in the lake of outrage but is still currently unobtainable. It most likely will be part of a future event like G-max Snorlax. By that logic you can assume that the others will be too. All Alolans forms have Pokédex entries (excluding cut Pokemon) that talk about their location in galar. Shield stating “ While it will guide travelers who get lost on a snowy mountain down to the mountain's base, it won't forgive anyone who harms nature.”