I stumbled on it when I was exploring switching between D and Dsus4 and Dsus2 and I find I really like the sound of it (especially just fingerpicking G, D and F#… and also switching between D and this chord.)
The note G that is a note additional to the D major triad (D, F#, A) sits within the first octave so would be called a ‘4’ rather than an ‘11’.
I have created a diagram to show three types of D chord with the note G added.
The first is a full triad plus octave of the root note and the G sits within the first octave so is a Dadd4. This is difficult to physically accomplish on a guitar. On a keyboard the adjacent 3, 4 and 5 would sound quite dissonant.
The second is the same chord with the note A removed so is - as @sclay states - a Dadd4 (no 5). This removes the immediate adjacency of the F# and the G and removes the A altogether. Those two aspects may be why it is pleasing to your ears.
The third is a full triad plus octave of the root note plus a G note added above that so is a Dadd11.