There is a building next to the POKeMART in Eterna City. Talk to the old man at the table in there and he'll rate your nickname and/or let you name or rename it.
Chat with our AI personalities
You can rename a pokemon by going to the Name rater
No, at least not according to what I've heard, and I've never found a way except deleting my entire save file.
Go to the namerater in Lavender Town or rename it right after you catch it.
Pokemon diamond
Unfortunately, you cannot nickname traded Pokemon in this game, or any Pokemon game for that matter. You can nickname your own caught Pokemon by going to the Condominiums next to the PokeMart in Eterna City and ask the old man near the entrance. I hope that you will make do!