Aeri is from the Korean ae (애 — love) + ri (리 — beautiful jade). Princess Aeri — modern Korean-American heritage naming.
Aeri 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 Aeri reduce to 6, The Nurturer. This is a traditional interpretive system, not a factual claim about the name.