Yep. It's supposed to be an entry level one. Ligustrum sinensis. In my old house had like 8 hours of direct sun and right now it only has like 2... I don't know what to do anymore.
The shadow is not really the problem. They love full sun, but can stand a lot of shadow. The lack of water or nutrients may be. Let it fully submerged in a bath for one hour. If is still alive, the bark or stems will turn greenish and new leaves may appear in a few days.
Sinense is semi caducifolious (if I remember correctly). Are you in spring or in autumn currently in your timezone?
(If you have pets take in mind that this is a poisonous plant with poisonous fruits only allowed for birds).