I say that after reading that article Obama assumes that the root of the nickname is Hawaiian.
What Toot believed kept her going were the needs of her grandchildren and the stoicism of her ancestors," Obama wrote."Anna Toot" whoever she was, was someone his mother and his grandmother knew of and admired enough to take her name as their own, to the extent that his mother was known by that name by her African In Laws and his grandmother preferred to be called by it.
I think there could be more to the grandmother’s nickname “Toot” as well. I agree that possibly she was nicknamed that before the family came to Hawaii. And later Stanley Ann used it as an alias.