The game takes place in the Orre region, which doesn't have traditional towns or cities with mayors. The closest thing to a mayor is Cipher Admin Evice, who runs the Shadow Pokémon organization. However, Evice is not the leader of Orre. He is only the leader of Cipher and serves the true leader, a mysterious figure known as "The Shadow".
It's possible you are thinking of a different Pokemon game, as many games feature mayors as part of the storyline.