The stiff tail feather used by penguins as a support when standing is a rectrix.
Rectrices are the large, stiff feathers of a bird’s tail. Penguins use their short, rigid tail feathers together with their feet to form a stable support when standing upright or climbing onto land and ice. Their tails can also assist with balance while moving.
Penguins have several adaptations for life in water, including streamlined bodies, dense feathers, and wings modified into flippers. Those adaptations make their tails less important for steering in flight than the tails of flying birds, but the tail remains useful on land.
A rectrix is not the same as a remex, which is a primary or secondary flight feather. Penguins lack powered flight, yet their feather terminology still follows standard avian anatomy.