Using a sub-glitch of Pomeg glitch, specifically a sub-glitch of Pomeg data corruption glitch and the News Reporter trick, it is possible to nickname Pokémon not originally assigned as belonging to the player (different OT/ID).
This glitch was documented by Tabbender and is achieved using a Fossil or a Generation II starter.
For this glitch you will need to know how to obtain any Pokémon or item with Pomeg glitch, which is shown in this video, and described at Pomeg data corruption glitch#Double corruption.
Steps
1. Double corrupt a Pokémon to obtain a Root Fossil or Claw Fossil as a held item (10 HP, 1 Speed, 30/31 Defense EVs on Horsea/Dots) and take the item (can probably be skipped if you already have a Fossil or access to the Generation II starter choices)
2. Double corrupt to get an instant Pomeg glitch Pokémon (194 HP, 40 Attack EVs on Horsea/Dots)
3. Arrange your party: instant Pomeg glitch Pokémon, Pokémon you don't need, Pokémon with Fly, Pokémon you want to nickname respectively.
4. Talk to the Pokémon News Reporter in Slateport City, to force an empty slot as the first Pokémon in your party after corruption from the glitch Pokémon's name.
5. Fly to Rustboro City and revive a Fossil. Choose to nickname it and you will be nicknaming the last Pokémon in your party instead, even if it didn't originally have your Trainer ID and OT.