Danai is from the Shona word danai — "love, to love" — common as a feminine first name in Zimbabwe. Her 2015 play Eclipsed — about five Liberian women during the Second Liberian Civil War — was the first Broadway play with an all-Black, all-women cast, crew, and director (Liesl Tommy); Tony Award nomination for Best Play.
Danai 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 Danai reduce to 2, The Peacemaker. This is a traditional interpretive system, not a factual claim about the name.