While the current answers say what d stands for, they don't really explain why D wasn't chosen instead. We could, for example, equally say that "D shows that it has deoxyribose..."
I offer this without any evidence (and without knowing whether such evidence exists). If you are interested in evidence, you will likely have to find the original article / work in which these were named, and hope that the author included some rationale.
AMP, adenosine monophosphate, is already an important biomolecule. Prefixing it with a lowercase d in dAMP suggests that it is the same as AMP, but just modified by a little bit (which is true; it just has one oxygen less). This is perhaps partly stylistic, but it also makes it easy to recognise visually as the small letter does not stand out as much. There are also other parallel examples, such as cyclic AMP (written as cAMP).