For a discussion of reactions of a natural product, I wouldn't have any problems with using 'dihydro' to indicate the change from diene to alkene, but I would stick to the IUPAC numbering system rather than calling it arbitrarily a 1,4-dihydro diene. For example, if the natural product was chrisr789ane and the diene was between the 13,14 and 15,16 carbons, calling the alkene "13,16-dihydrochrisr789ane" seems to me to be good enough. Then you could just add the substituents, eg "13-methoxy-16-sulfonamido-13,16-dihydrochrisr789ane"