Due to some interesting quirks in Pokémon Red and Blue, every Farfetch'd across every copy of the game was named «DUX.» While it may not have been a purposeful decision by Nintendo, a few game mechanics working in tandem ensured that this was the case. No matter what the player did, there was no way to change this seemingly arbitrary fact.
Farfetch'd is a Pokémon with a rather interesting history. In Pokémon Red and Blue it was actually one of a kind, and could only be received through an in-game trade. However, despite its rarity, it was not very strong, and arguably worse than the Spearow it was traded for because it couldn't evolve. However, its scarcity still made it a common curiosity among players. In later generations, it would get an Attack boost, and in Sword and Shield it even got a Galarian form and evolution, Sirfetch'd. Red and Blue Farfetch'd had none of that, though, simply being a relatively weak bird Pokémon.
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There is only one Farfetch'd that the player can receive in Pokémon Red and Blue. By trading a Spearow to a specific NPC in Vermillion City, the player will receive a Farfetch'd in return. With Spearow being quite common, it would be rather easy for the player to have caught a spare for the trade. This Farfetch'd will always be named DUX, and because there is nowhere in the game where a Farfetch'd can be caught, this trade is the only way to get one. Thankfully, this trade is much fairer than Mindy of Diamond and Pearl's Haunter trade, but it does mean players who hate the name DUX don't have any other option.
However, there is a way to change a Pokémon's nickname that has existed even as far back as Red and Blue, and that is the Name
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