Eileen is the anglicized Irish Eibhlín — a Gaelic form of Helen, from the Greek hēlē (sun, light).
Subject of Peter Adam's Eileen Gray: Architect/Designer (1987).
Eileen 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 Eileen reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.