Alkyone (Ἀλκυόνη) is the Greek word for "kingfisher." Daughter of Aeolus, wife of Ceyx — both transformed into kingfishers when she leapt into the sea on hearing of her husband's drowning. The "halcyon days" are the two weeks around the winter solstice when Aeolus calms the seas for her brooding.
The English word "halcyon" preserves her name.
Alkyone reduces to nine — the number of Greek halcyon.