Iris, directly from the Greek iris, rainbow. Aristotle also used the term to describe the bright halos that sometimes encircle the moon.

Rainbows and halos: no wonder the Danish anatomist Jacob Winslow, in 1721, chose to call the pigmented, circular arrangement of smooth muscle that surrounds the pupil the iris. Though it was with this coinage that the term become firmly established in anatomy, the Greek author and physician Rufus of Ephesus also called this part of the eye the iris a full 1,600 years earlier, apparently unbeknownst to Winslow (Ephesus also named the optic chiasm).

A lunar iris, per Aristotle www.pixheaven.net

Iris was a Greek goddess before being a rainbow: a messenger among the Greek pantheon. Iris became associated with rainbows because they were a symbol of good news in Greek society and she apparently brought her fair share of welcome reports.

The Goddess Iris. Detail from ancient Greek clay vase. Photo from Sotheby's London F15923. © Sotheby's