Irini is from the Greek Eirene (Εἰρήνη — peace). Irini is the modern Greek form of Irene / Eirene — central to traditional Greek Orthodox heritage. The Greek Eirene is one of the Hours (Horai) of Greek mythology — daughter of Zeus + Themis + goddess of peace alongside her sisters Dike (justice) + Eunomia (good order). Saint Irene of Athens (Empress Irene, c.
Irini 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.
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In Pythagorean numerology the letters of Irini reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.