In Pokémon Sun Moon anime, now that Pokémon League Champion is Ash and there are no Elite Four, does this make Ash the Pokemon Champion of Alola?
Yes, Ash is now considered a Pokemon champion of Alola like Steven.
However, Ash already was a 'champion' before becoming the champion of Alola, the champion of Orange Islands.
However his victory on Orange Islands is often disregarded due to the unconventional 5 gym battles without Elite Four, a Champion, or a Conference.
As mentioned on the Pokemon fan Wiki the following is required to become a champion
A Pokémon Champion is a trainer who has beaten a region's Gym Leaders (in Alola's case, all 7 trials and totem Pokemon), Elite Four, and the previous Champion.
Yes, He is one of the regional champions now because this was the first league of Alola region. He is now the one step closer to become a Pokemon master. He will get the official invitation for the next champion's league tournament where he will battle against the regional champions. If he wins then he will be considered as a Pokemon master by the world.