Hmm, characters that Id' like to see in Sun & Moon, huh?
Let's see, first of all I'd like to have another female professor and also, together with her, a female evil team boss.
To make things more interesting, they could make both of them old friends, whose reasearch objectives were the same at the beginning, but that in the end, with the passing of time, ended up going in two different directions, leading one to become a succesful Pokèmon professor and the other to form a criminal syndicate who would further her research and do her bidding.
I think this would involve more the professor in the story and would give more depth to the plot altogether.
As for the other characters, a jerky rival wouldn't be so bad and I'd also like to see characters from previous games, for example Shana, who in XY told us that she had the intention of travelling to another region.