In the II generation games that takes place in the Johto region the league called... be prepared, the Indigo Plateau, together with that there's to be mentioned, in the games the Pokemon leagues called.... the Pokemon league. That to be said, GenII games are known to be continue for the 1st gen games, occurring on the same land two years after the first games, dividing the land to two different regions, and the johto league is the same as the Kanto league just different Elite Four and champion that changed over the years, so in the games to be called "the Indigo league" though not to called that way in the games can be true as it serves the league for two regions and not to be a one region Pokemon league only as in the next games (though the League lies in the Kanto region borders).
Now, if the anime were more closely to the games it will be the same so calling it the Indigo league will make much more sense why called differently than the other regions, but the anime didn't adapt that closely but placed the Johto Pokemon league in Silver Conference at Silver Town.
But while at it, the announcer of the anime says clearly the the indigo plateau is only the home of the Pokemon league and not calling it "the indigo league", and so on in the first season it's only being said that the Indigo plateau is holding for a fact the Pokemon league for the Kanto region.
That point of view leads to Wondercricket answer, I will quote the main part:
In the Generation I games, the final area of the game is called
"Indigo Plateau" which lead to many players assuming the Pokémon
League for this region was called the "Indigo League".