A..different idea, not sure if these things have been used often..or if at all. But yeah, adopted it from the lovely Leargini on furaffinity , so why not?
Kleopatra was born to a widowed mother, her father lost to hunters. Her mother warned her of those that hunted unicorns..especially unicorns such as their kind; those that could grow things. Some could grow plants or vines, some could shove their hands to the earth to bring forth rare minerals. Their kind could grow mushrooms of any sort. Medicinal, rare, culinary, deadly, etc. Of course, they expended calories and energy to do so, but the cost was usually worth what they grew.
Once she came of age, she began to feel the effects of the moon. It pulled at her, changed her alongside its phases. From female to male, and from male to female, their body growing stronger or weaker, more confident or more shy. When the moon is full, she is as she was born; female. On a new moon, when the great orb is hidden, she is the reverse; male. As the moon wanes, her body grows stronger as her clit grows into a larger rod, one of her ovaries becoming a testicle. However, she grows more shy. As it waves, his body grows weaker, their rod resuming it's natural shape. Now having two inner testicles, one drops to become an ovary, the other following once the full moon is nigh.
When female, she prefers to be called Kleo. When male, he is fine with either Leo or Pat.
After a few years of adapting to these cycles, her mother was lost to her in a storm. She wept as the great unicorn became as a tree stump, mushrooms sprouting across the stunted wooden body. She'd no longer be hunted, but she would no longer be able to aid her daughter.
For further elaboration on gender (just to make things a bit more clear), they're fully female on and briefly around the full moon, a hermaphrodite while the moon is waning, and a shemale while the moon is waxing.