The Province du Dauphiné was a region of France near Switzerland, the people living there were called the Dauphinois, hence the name of the "Gratin Dauphinois". Personally, I cook it with cream only and it gets enhanced by a touch of grated nutmeg. There is also a "Gratin Savoyard" from the nearby Savoie region, (funny
enough the people there are called Savoyards) where the cream is replaced by
milk and cheese, sometimes 1/2 cream, 1/2 milk. The cheese used is always a Swiss cheese, either Gruyere, Comté or Emmenthal.
The Prince Dauphin was the title attributed to the eldest son of the kings of France and has nothing to do with the gratin. Dauphin in French also means dolphin and it definitely has nothing to do with the gratin!