I would like to change the name of my Pokémon in my Moon version, but I have no idea where I have to go for this. Is there any NPC who can change your Pokémon's name like in the previous games, and where can you find him?
There is indeed one character who can change your Pokemon's name in the game, the Name Rater. This NPC can be found in Heahea City on Akala Island (the second island of the game). He is located in the second building you can go to when you are leaving the boat, the Alola Tourist Bureau.
You then have to talk to the old character on the right with a blue and yellow shirt. He will present himself as the Name Rater, and you will be able to change your Pokemon's name.