It's not a real word in the dictionary. It was probably the easiest word that Nintendo could find as a translation from their Japanese name while maintaining a cool sounding name.
Notice how it can be split into Arch - Djinn, which are both words by themselves? Arch meaning the most important/extreme (like Arch-mage), while Djinn being a supernatural creature in Arabic Mythology, also called Genies.
If you take a look at the Japanese name, there's a bit of Kanji in it which can be translated to basically, Super Genie. That's probably where the name comes from, as an English Translation - and let's face it, Archdjinn of the Rings: Hoopa sounds better than Super Genie of the Rings: Hoopa