Hermione (Ἑρμιόνη) is the feminine of Hermes — "messenger." The only daughter of Helen and Menelaus — left in Sparta when her mother fled to Troy, later married to Neoptolemus and then to Orestes.
Hermione 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 Hermione reduce to 6, The Nurturer. This is a traditional interpretive system, not a factual claim about the name.