Origins & Name

Further, because Darkrai is highly associated with nightmares, its design may also represent just that. Darkrai actually kind of reminds me of Pitch's nightmares from the Rise of the Guardians movie. They are dark, wispy figures that can come and go from the shadows, much like Darkrai. These nightmares are the physical manifestation of fears. Darkrai itself is feared and hated by most people and Pokémon, at least in the beginning. Perhaps it was designed to physically represent that fear as well.
Darkrai's name is the same in Japanese, English, Spanish, French, German and Italian! It's likely the name "Darkrai" is a combination of "dark" and 暗い (kurai), which is the Japanese word for dark. Considering Darkrai's classification as the "Pitch-Black Pokémon," this interpretation would certainly make sense. I've also read another interpretation of the name as a combination of "dark" and then the Hindi word for king, "rai." Darkrai is the only legendary Pokémon that is solely a dark type and thus could be considered the "king" of darkness!
Lunar Duo

Drawn from Darkrai's relationship with Cresselia, it can be said Darkrai is related to the new moon. In fact, Darkrai is actually said to be active on nights of a new moon. When the moon is considered "new," it cannot normally be seen and therefore the land is not illuminated. Everything is dark and it's more difficult to see clearly than when there is a full moon or even any of the other moon phases. Considering Darkrai is the Pitch-Black Pokémon, this fits it very well. Darkrai would want to move around in the shadows in order to avoid being seen by others. It is a feared and hated Pokémon, after all. Having no light in the darkness could also be symbolic for experiencing nightmares. Cresselia, being connected to the full moon, would be the Pokémon to light up the darkness. Such a symbol is certainly connected to its role of protecting others from Darkrai's nightmares.
Friend or Foe?
Is Darkrai a good or a bad Pokémon? The Darkrai in the tenth movie was clearly good, but what about the Darkrai in the main game series or in the anime? Further, Darkrai is the main antagonist in some of the Pokémon Ranger games! Like it has been said in the anime series, though, I don't think any Pokémon is inherently bad. I feel this is especially true for Darkrai.
If you look at the majority of Darkrai's Pokédex entries, you will consistently see "but it means no harm." Yes, Darkrai makes people have horrific nightmares by using its Dark Void attack. But it doesn't do it in a malicious way. In fact, Darkrai is only protecting itself and its territory! Additionally, simply falling asleep near a Darkrai causes people and Pokémon to have nightmares. People will fall into nightmares even if Darkrai doesn't act consciously. Is it really its fault, then? After the player captures Darkrai in DPPt, a mysterious voice will comment on how Darkrai can't control its power and how it secludes itself to Newmoon Island in order to protect people and Pokémon from itself. Further, Fullmoon Island is close by if someone does happen to be inflicted with nightmares. Clearly then, Darkrai makes a conscious decision to stay away from other living creatures because it doesn't want to hurt anyone. It chooses to live a life of loneliness to prevent harm it can't control. Therefore, despite darker roles in some games and one of the anime episodes, I don't think Darkrai is a bad Pokémon. It is simply misunderstood.
Why Darkrai?

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