Iris is the Greek word for "rainbow," and in Greek mythology Iris was the goddess and personification of the rainbow, who served as messenger between the gods and humans. She is often depicted with golden wings, carrying messages from Olympus down to earth along the arc of the rainbow. The flower we call iris was named after her, for the many colours its petals can take.
The name has been used in English since at least the eighteenth century, but its current rise is a contemporary phenomenon.
Iris does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
In Pythagorean numerology the letters of Iris reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.