Here in the Land of Clinton we call this tree a Possum Haw. I have heard the botantists at the university call it a decidious holly. Several of these tress are growing in my yard and in the surrounding woods. We didn't cut them out even though their growing habit does not conform to the tastes of most gardeners. It tends to be "weedy" looking. But my goal is to have a yard full of native species, not one created from a textbook. It takes less water, fertilizer, and money to garden this way. Another reason the trees have been left here is because as kids we picked berries and strung them for decorations on the Christmas trees. So when I look at these trees, I recall pleasant childhood memories.
For some reason this year the birds haven't eaten all the berries off the trees. I don't know if it is because we are feeding the birds high dollar bird feed, if more people are feeding the birds, or if there are fewer birds. At any rate, I am pleased that the berries are so colorfull on gray dreary days.