Ainhoa is from the Basque — referring to the iconic Marian shrine village of Ainhoa in the French Basque Pyrenees. Princess Ainhoa — Basque heritage naming.
Ainhoa 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 Ainhoa reduce to 3, The Communicator. This is a traditional interpretive system, not a factual claim about the name.