What does the letter "D" next to the VOR frequency and name mean?
Since you're specifically referencing a Jeppesen chart, we'll go right to the source.

Jeppesen's "Introduction to Jeppesen Navigation Charts" has a glossary and explanation of all terms and symbols.

The answer to your question reads as follows:


  1 — VORDME. Low and High/Low charts include a Compass Rose with VHF
  Navaids. Shadow box indicates navaid is airway component, with
  frequency, identifier, Morse code and INS coordinates. Small "D"
  indicates DME/TACAN. Class indicated by: (T) Terminal, (L) Low, (H)
  High.


So, the D indicates that the VOR has a co-located DME radio. 

(and, no need for correction to your assumption: the H and L in brackets do, indeed, refer to a High or Low class of VFR)