I grew up in a "Little Italy" neighborhood, and all of my ancestors hailed from Italy. And I never came across the name "Chastity" among Italians.
I think Sherman is right that it's an old-fashioned American name. It's a beautiful name, but, yes, a young girl probably would be teased about it in modern times.
Chastity, Hope, Prudence, Obedience, Charity. All pretty common names in the old days.
My personal favorite, though English Puritan rather than American, was the son of Praise-God Barebones who he named If-Christ-had-not-died-for-thee-thou-hadst-been-damned Barebones.
Oddly, he chose to go by the name Nicolas when he grew up. Made a name for himself as an early economist.
His brother was named Jesus-Christ-came-into-the-world- to-save Barebones.