The name of the recipe comes from the name of the pan. Earthenware pans are the traditional cooking, as well as serving, vessels for paella, and will hold the food hot after cooking. However pans made of steel and other metals have become more popular, due to their prolonged durability.
Steel pans are easy to handle, and quick to heat. Frequent stirring helps to insure even cooking. After you're done cooking, be sure to wash and thoroughly dry the paella pan, then put a light coating of oil on it before storing, to help prevent rust from forming. Blued steel is carbon steel that is heated so that the surface oxidizes and forms a dark, bluish coloration; it serves to help protect -- but not prevent -- the pan from rusting. (Stainless, earthenware, and enameled pans do not need oiling before storage.)