It actually does mean Dolphin...

Dauphiné was a feudal region in what today is France but was at the time technically part of the Holy Roman Empire. It's lord had taken a Dolphin for his crest and arms (think Richard I's leopards or the German eagles); subsequently his descendents took the nickname and it was incorporated as the name of their holdings.

About two hundred years later, Philip VI of France bought the region and title from its lords and granted it to his grandson, not his son. After this grandson (future Charles V) was crowned, the title was passed down in a similar fashion to that of England's Prince of Wales title.

Edit: Just thought, not really sure what happened to Dauphiné, as in it was Imperial but also a French holding that must have been incorporated...