No research has gone into this claim, but it would be an awesome name.
Also it would follow Microsoft trying to keep up with PS4, as Delta looks kind of like a 4. (Capital at least)
Then people could do those conspiracy pictures (X, X; Square, Box; Circle, 360; Triangle, Delta) pictures with completion...
And Xbox Delta rolls off the tongue.
(Microsoft people, if you're browsing this forum, this one's on me.)
Oh, also, the way that they could justify it is through the definition of delta as a landform at the mouth of a river, as it brings together all sorts of media (gaming, movies/TV, music, etc) I mean hey, it's no less far fetched than the 360 holding its breath.