This is a question that's always kind of rolled around in the back of my mind, because I've never seen any discussion of how these coinage "heads" were actually made and what people worked from. Do we have, for example, cases where the head wasn't changed, but just the name? This potentially applies to a huge swath of land and a vast reach of time, so I'll slightly narrow it to "400BCE to 500CE, eastern Mediterranean" for argument's sake.
The ancient Greeks definitely had a tendency to idealize their portraiture according to their own aesthetic. Alexander the Great was one of the first to put his own image on currency, and he often showed himself with the skin of the Nemean lion(to liken himself to Heracles), as well as with the horns of a ram, suggesting a legend he propogated that he was the son of Zeus. There is more variation in later Roman coinage portraiture, particularly after Julius Caesar. Augustus, for instance, often depicted himself years younger in his coinage, as well as in other artistic depictions such as sculpture. Others gave a reasonably accurate depiction of themselves, in keeping with the Roman realist style, but like Alexander the Great, they would add attributes or accessories to associate themselves with the gods.