With only a pair of E's and a B, what chord symbol are you going to put to it? It's sort of an E chord, but what kind? Dunno. It takes a G to identify it as an Em or a G# to identify it as an E (major).
I'd probably write it down as "E", and stick a note explaining that that means an E diad, or something like that. There's bound to be a symbol somewhere that means that, but I suppose most people wouldn't recognise what it means.
Just so long as we don't have to feel obliged to stick that 5th in just in order to have a name for it.
It sounds as if I've been using "power chords" all along and didn't know. Can't say I like the name. Why "power"?
But here's another query - if you play a chord up the neck, and then work out which strings you would leave open if you were playing it down at the nut end, and then you play them open anyway - what do you call that? It gives you some good sounds to play around with.