It is named for the circular short-sided pan in which it is cooked. The Paella or pan comes in many sizes from two servings to the giant 12 servings. It can also be cooked in an iron skillet, Pyrex or Corning Ware baking dishes.
Paella has many variations.
In Madrid, it will contain vegetables, chicken or rabbit with rice and saffron. In Valencia it will contain Fava Beans and small grilled land snails, called Caracoles. In small villages, it will be little more that baked rice and saffron with small bits of chicken. Towards the coast, it will be heavily laden with shrimp, lobster and mussels or clams. This is my variation and, hopefully, simplified for home use.