The original Fire-Eye preamp was the Red-Eye, so named for its big red boost button. But what if you wanted to make a simpler version of the Red-Eye preamp, preserving all its great DI features, without the boost and extra preamp features? Well, what you'd be left with is a world-class DI.
But what to name it, since all your other products end in "eye"? Ah, yes: The "Dee-Eye". Because it's a DI. Now, whenever anyone says, "You should get a DI", it will sound like they're saying, "You should get a Dee-Eye." Daren, using a simple trademarked name, has just made everyone recommending a DI sound like they're recommending his product. Genius.
Oh, and the Dee-Eye is awesome, too.