What is the name for a female zebra?

A female zebra is called a mare. Zebra herds have a dominant mare who leads the other mares and their foals. African Wildlife Detective states that an alpha mare defends her right to dominance by fighting and aggressive gestures.

The dominant mare has first pick of dust baths, shade and water, and she shows her dominance by lowering her head, laying back her ears, baring her teeth and lashing her tail. Zebra mares are pregnant for 12 to 13 months and usually give birth to one foal at a time. The mare keeps all other zebras away from her foal for a couple of days until it recognizes her through scent, sight and sound.