One could say the 3rd is implied because the key is D Major. Even though the G note is "missing" for this fingering, it wouldn't drastically change the character because the tritone dissonance between E and Bb dominates the sound. In other words, if one were to stretch the fingers to play 075300 ... that extra G is drowned out by the tritone.
The notes are E, B, E, Bb, B, E
I would say E7(b5 no 3rd) or maybe Bmaj7sus4
You could cal it E5 add #11 I guess. I figured the g was implied because of the key but not necessarily I suppose. I use this chord in a few of my songs albeit in different keys. In one it resolves to a major. In another it's minor.
C, an E-flat, and G go into a bar. The bartender says: "Sorry, but we don't serve minors." So, the E-flat leaves, and the C and the G have an open fifth between them. After a few drinks, the fifth is diminished: the G is out flat.
An F comes in and tries to augment the situation, but is not sharp enough. A D comes into the bar and heads straight for the bathroom saying, "Excuse me, I'll just be a second."
An A comes into the bar, but the bartender is not convinced that this relative of C is not a minor. Then the bartender notices a B-flat hiding at the end of the bar and exclaims: "Get out now! You're the seventh minor I've found in this bar tonight." The E-flat, not easily deflated, comes back to the bar the next night in a 3-piece suit with nicely shined shoes.
The bartender (who used to have a nice corporate job until his company downsized) says: "You're looking sharp tonight, come on in! This could be a major development." This proves to be the case, as the E-flat takes off the suit and stands there au natural. Eventually, the C sobers up and realizes in horror that he's under a rest. The C is brought to trial, is found guilty of contributing to the diminution of a minor, and is sentenced to 10 years of DS without Coda at an upscale correctional facility.
So EmAdd#11 feels right althought EmAdd#11(no 3rd) or E5Add#11 is probably technically correct.
The last 2 that explicitly excludes the 3rd is not necessarily more "correct" -- that notation simply biases the consequences of the fingering mechanics on a fretboard.
The EmAdd#11 is also correct because intellectually, emotionally, contextually, etc ... it's an E minor sound in your D Major key song.
If you had a 7-string guitar, or were pressing 10 fingers on a piano, you may very well have included that G note (the 3rd). The problem with the supposedly "more correct" E5Add#11 is that it inadvertently states that you deliberately excluded the G as a compositional decision instead of a fingering one.
So, if you were communicating that tonality to another musician without regards to physical limitations on instruments, I'd be more accurate to say EmAdd#11. On the other hand if you transcribing traditional notation without any tablature, then the E5Add#11 is more precise because it lets guitarists know that they don't have to stretch their fingers for that elusive G that's supposed to be there.
I have no quarrel with calling it Emadd#11 but if writing a chart myself I would call it Em#4 or Em#4 no third depending on whether it was for the tune as a whole, or just the guitar part.
IMO - in my world - #11 implies more of a jazz voicing where the A# would be spaced far apart from the B, or the B would be omitted. So #4 better conveys the b9 interval clash that is a main feature of the chord.