Posy is the English word for a small bouquet of flowers — also a diminutive of Josephine.
Posy is rising in modern British naming. Posy Simmonds (born 1945) is the British cartoonist (Tamara Drewe).
Posy 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 Posy reduce to 3, The Communicator. This is a traditional interpretive system, not a factual claim about the name.