if I have a chord made up of the notes:
D F# G# B
I can write that as a Bm6/D, but can I write it as D#4add6? How would you write this chord as a D chord, or is there no way to
Bm6/D is your best bet. It's clean, specifies all the notes, and won't encourage anyone reading it to add in extraneous notes. Yes, D(#4add6) is probably as good as you're going to get if you're insisting on D being the root. If there was also a C# in there, no one would blink twice at a 13 and #11 in there, but the #4 and 6 are definitely odd without a 7th and might confuse someone who, for example, saw that chord while comping. If you don't value specificity too much, you may be able to get away with calling it a D Lydian chord. I've heard odd chords named after the modal tonalities they imply, so maybe that works for you.
It makes me feel good in my soul to call it a G#m7b5/D. The problem with this is that I doubt it's actually functioning as a half diminished chord and having a b5 in the bass is unusual. I'm interested in how you've voiced this. D being in the bass with these notes, though, says to me that it's acting like a D Lydian chord or a Predominant chord in A.
If we consider it a D chord, D (b5) add6 seems to me a more natural way to name this chord, a D major chord with the lowered 5th and the added 6th.
But the name of the chord, despite having D in the bass, should consider the harmonic function it is fulfilling. For example, say it is working as a Subdominant in the tonality of F#min, then it would be more proper to call it Bmin (even if in first inversion, in this case). [Thanks to Tim for correcting the mistake in the initial example I provided.]
To my ear, when heard alone, it definitely sounds as a minor chord, so without contextual information Bmin add6 would be my choice.
If this chord functions as a D chord in the context of the chord changes (ie: progression), then I would write this as either a D13 (#11), or a DMaj13 (#11), both of which are commonly used in jazz.
In my experience, a sharp-11 is a more common extension of a Maj 7 chord than a dominant 7, because it simply extends the Major-third/minor-third pattern of building the chord. But I have certainly seen sharp 11's used in dominant chords.