Annunziata is the Italian word for "the Annunciation" — the announcement by the archangel Gabriel to the Virgin Mary that she would bear Jesus. A traditional Italian Marian name.
Annunziata is widely used in Italy.
Annunziata 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 Annunziata reduce to 4, The Builder. This is a traditional interpretive system, not a factual claim about the name.