Clinton,

0x000x is an E-7 (Em7) so doubling the E by playing 0x0000 would still make it an E-7. Dropping the normal B to an A to play 000000 might be called an inversion of an E-11 (Em11). The 9th is missing and the 11th isn't on top but I think E-11 is a valid name for the open strings played as a chord.

I actually use this in the E-7 form but I play it an octive higher as (12)x(12)(12)(12)x noting the bass E with the middle finger and catching the rest with a ring finger barre.

Of course, thanks to inversions, E-7 is also G6 and A would be the 9th so I guess the open strings could also be called G6-9 (G six-ninth).

      - Mark