The OP has asked for an AIP reference for his question, and as far as I can see no one has found one (me included). Can anyone find a reference anywhere? I can only recall (don't have the AIP to hand) mentioning of the naming convention used, when this was introduced in Australia a while back, possibly in a now expired AIC or SUP.
Is this another example of our awesome regulations in Australia - folklore and local familiarity begets procedure that turn into proxy regulation (ie. the only difference is the DME, so if Approach don't specify, you can do whatever you want... [drawl] "Yeah that's just what we've always done, it must be right"[/drawl].)
As for those saying "the only difference is which DME" well I think you're missing the point somewhat. That may apply in this specific case, but I reckon it's fair to say that the OP is looking for a more general answer, that could be applied in all cases.
And if there's any doubt, of course without exception, you would ask!