Looks like Celtis australis. It has the asymmetrical leaves typical of Ulmaceae and it has berries versus winged seeds that would be typical of Ulmus and Zelkova, our other common Ulmaceae trees.

I can't see any potential disasters from that photo; why do you think the tree is going to come down or must come down?

Joe

Its has woodpecker damage all the way about halfway up and all the way around all main branches. When the winds blow it really shakes. Just in case they decide to take it down I want to be prepared but I doubt they will.
Its my only shade from the S so don't want to lose it but don't want it falling on someone elses home either and wrecking fencing. Its also a bird haven and the owls like it.

I was thinking it might be a Camphor Tree = Cinnamomum camphora.

I doubt the woodpeckers have done much damage to this hearty tree. What you have is a lovely tree that looks to be well balanced..... and is just getting big enough to be great for shade. It grows slowly to 50 feet tall by 60 feet wide.

Funny you mention that Westelle cuz I have a camphor tree in front and isn't quite the same.
The camphor sheds leaves and branches twice a year and never goes completely bare like this one does and the berries are bigger than these are.