Caelestis suggests below that the abbreviation stands for ‘donum dat/dedit’. I was looking through the epigraphy book mentioned below and have found some confirming evidence. In it is reproduced an inscription from an obelisk in Rome:
IMP.CAESAR.DIVI.F
AVGVSTVS
PONTIFEX.MAXIMUS
IMP.XII.COS.XI.TRIB.POT.XIV
AEGVPTO.INPOTESTATEM
POPVLI.ROMANI.REDACTA
SOLI.DONVM.DEDIT
And here are a few more abbreviations (the second of which lends support to Dennis’ suggestion ‘dedit’) listed in chapter 7 employing the letter ‘D’:
D: dat
D, D.D: dedit
D, DED, DD: dedicavit
D.D.D: dedit idemque dedicavit
D.D: dono dedit (is dono some sort of predicative dative here? Or is this a parallel construction to one in which we would find the accusative of the person and the ablative of the thing (cf. Allen & Greenough 225d)?)