i think it is beautiful the way it is. All natural. I'd leave it it if were mine)

I would leave it as is, it looks like there is plenty of room in the pot. If you were to divide it keep it in sections of 3 at a minimum.

As long as the canes are green they are providing energy to the plant. If you need to remove them at some point to fit into a pot save them. There’s a good chance they will sprout a new plant from a dormant eye.

It looks like a dendrobium to me.

Not a Cattleya. James is correct. You have a Dendrobium.

I wouldn't do a thing. Leave the leafless canes. That is how they grow and look. Those canes are supplying support for the other canes. When they dry up you can remove them.

Jane

Thanks everyone--and thanks on ID'ing it!