It seems likely that Anona could be a combination of existing names like Anne and Fiona. Ona could be used as a short form for Anona. (Source: Hanks, P. & Hodges, F., (1996), Oxford Dictionary of First Names, Oxford, United Kingdom: Oxford University Press, pages 22 and 256)
I was told years ago Anona means "little princess" in Cherokee Indian according to my mother who did name me after her labor and delivery nurse. The nurse was Cherokee Indian.
(Source: Hanks, P. & Hodges, F., (1996), Oxford Dictionary of First Names, Oxford, United Kingdom: Oxford University Press, pages 22 and 256)