leeneia - you've misread the 1st note there - it's a D# not a D (otherwise you would be correct).

The chord (as is) can be read as either an F#m6 or a D#m7b5 ('half-diminished'). B9 without the root is a reading but less likely in A (unless it then moves to E7 or E9).

As has been pointed out above, you really need the context to decide how to assign a name to the notes. If your A chord has a C# in the bass, then it's a nice 1 step bass move to D#m7b5. Or if you have an E in the bass of the A it's a nice half-step down to D#m7b5. If your A chord has an A in the bass, then you might be thinking of A-F#m6-Bm7-E7 (I-VI-II-V).

Mick