Wax Leaf Ligustrum, Ligustrum japonicum.

It's okay to hard prune it. I've cut several down to stubs and they roared right back. They are invasive in the mid Atlantic, so I cut down the big ones which came with our current home. Now they are kept at six feet tall so I can easily dead head.

Thank you both for your wisdom! Now onto pruning them up!

If you whack it today, it may not grow back much before spring. If you like to string holiday lights, keep it an appropriate size for decor this winter and lower it in spring.