The name of this is on the tip of my tongue, I know it but can't remember it. I use to have a bunch of these growing along my fence at my old house. I'll see if I can find the name.
Edit: I believe it is a type of privet, not 100% sure however.
It's definitely NOT oleander. I grew up around that bush and could spot it from a mile away. Are the leaves waxy? Also what do the veins look like?
Look up bay laurel or sweet bay. By photo, they have a lot of similarities. Good luck!