True, it makes sense to call it F#m7b5 in the key of E.

It will sound the same either way though, of course. So, if you are just using it for accompaniment, it really shouldn't make a lot of difference what BIAB calls it. You know it is the same chord.

I can see, however, if you want to print out a lead sheet, and want it to read as clearly as possible, that you would prefer it call the chords by the more common way of naming them, according to they key.