Irene is from the Greek eirēnē ("peace") — also one of the three Horae (goddesses of the seasons and natural order) in classical mythology. Empress Irene of Athens (c.
Irene 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 Irene reduce to 6, The Nurturer. This is a traditional interpretive system, not a factual claim about the name.