Tui

Origin: Māori
Gender: Unisex
Meaning: The name of a bird native to New Zealand
Pronunciation: TOO-ee
Other forms: N/A

I know there aren't that many, but I'm a person who is totally obsessed with birds of all kinds. I myself own a cockatiel named Icarus (but just called Birdie), have owned a parakeet, and plan on owning birds for the rest of my life. I also love wild birds, and have recently discovered the name Tui, which is used as a name, and is also the name of a bird from New Zealand. The Tui, which was called the "parson bird" by European colonists, is one of the largest birds in the honeyeater family. 
At first glance they may appear to be solid black, but they actually have a beautiful iridescent sheen, and some brown feathers on the back and flanks, along with a collar of lacy white feathers around the neck. Tui have two voice boxes, and along with being as intelligent as many parrots, are able to make an assortment of noises and calls, and even imitate human speech. The Māori would sometimes capture and tame them, and teach them greetings and prayers and even how to sound like their chief - they would call those birds "a manu rangatira" - a chiefly bird. 

Tui as a name is unisex, but much more common for girls than for boys. Tui Sutherland is one of the authors of the popular kid's books series "Warriors".