Fatsia japonica.

It can grow to a large shrub/small tree. It's not a herbaceous perennial to be cut back annually.

Fatsia japonica "Japanese Fatsia" The article linked below has some good info re: growing conditions, etc.

Here is a link that might be useful: Fatsia japonica

Aralia (or Japanese Aralia) is the common name often seen at nurseries around Texas... and other places, I'm sure. They don't seem to get much over four feet in Dallas except where very well sheltered because nature prunes them back every 2 or 3 years with a hard freeze.