The name changer guy is in eterna city next to the pokemart
you go to eturna city(sorry i spelled that wrong) then in the bottom right kinda, the name changer is the old dude in the big building.
In Jubilife City
Lavender Town.
The name changer is in eterna city there will be a sign Which is the old man in the building next 2 pokemart LuciLicious - If the mew is imported from a game or from PokeRanch or somewhere else and wasn't originally the trainer's in pearl/diamond you cannot change the name.
lavendar town.
the name rater is in goldenrod city to the left of the third gym (Whitney)
In the large building in Eterna City on the first floor. He is the old man. Remember, you can't change the nickname of a traded Pokemon.
In lavender town
Slateport in front of the contest place
In eterna city he is a old man in an apartment building he claims he is a name rater select the Pokemon to rate the name then he asks you if you want to change it
On every Pokemon game, there is a name changer. He will allow you to change your Pokemon's name, either with a small fee, or free of charge.