Yes, I call it anón. Some people call it cherimoya. Cherimoya is also used for Annona cherimola in South America and in Cuba it is used for Annona reticulata.

Good question. They are a different species. Sugar apple is "Annona squamosa." Cherimoya is "Annona cherimola." Atemoya is a cross between Annona squamosa and Annona cherimola. A. squamosa fruits well in Florida and low elevation areas. It is smaller and more seedy than A. cherimola. A. cherimola only flowers and fruits in high elevation areas. They are native to the mountains of South America and there are some commercial growers in California. Atemoya is larger and less seedy than sugar apple and it can also flower and fruit in low elevation areas like the sugar apple. In Cuba the fruit Annona reticulata is called cherimoya, but some people call that custard apple. It is easier to use the scientific names as Annona species have a lot of different common names that conflict.

How interesting I never considered that the fruit would change color while still on the tree when it is cold outside!

Yeah it would be! It isn't that accessible because it is difficult to ship it without it getting damaged.