Alanis is the feminine of Alan — possibly from the Celtic ailín ("rock, little rock") or Greek alanos ("harmonious") — used as a 1970s North American given name. "You Oughta Know" (1995), "Ironic" (1995), "You Learn," "Hand in My Pocket" — Jagged Little Pill is on Rolling Stone's 500 Greatest Albums of All Time. The Broadway musical adaptation Jagged Little Pill (2019) won the Tony Award for Best Score and was nominated for Best Musical. Alanis Mitchell — Mythological reference.
Alanis 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 Alanis reduce to 2, The Peacemaker. This is a traditional interpretive system, not a factual claim about the name.