There are not exclusive names for the female penguin, but they have been called hens. Most of the time they are simply referred to as the female penguin.
The Emperor Penguin females lay the eggs. The male penguins keep the eggs warm, while the female goes to eat fish, krill and squid. When they return, parenting duties swap, and then the male goes out and eats.
The female Chinstrap Penguins lay two eggs and switch off incubating with the male penguin until the eggs hatch. Once the eggs hatch, the penguins share the foraging and feeding responsibilities, unlike some of the other penguin species.
The Macaroni Penguin females lay two eggs, and she and the male rotate incubating until the eggs hatch. She then goes for food, as the female penguins are the foragers, while the male is the protector.