Dione is from the Greek Διώνη (Diōnē — divine, goddess) — feminine of Zeus / Dios (god). Dione is one of the Greek feminine names — central to traditional Greek mythological heritage.
Dione 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 Dione reduce to 2, The Peacemaker. This is a traditional interpretive system, not a factual claim about the name.