It's not the headphone, it just plays what the phone sends it. It's the phone. If you have something that announces the caller verbally, it should go to the headphones if your media channel is going there. (If it's coming through the system channel, it probably won't, though.)
But if you're running Oreo you probably need an app to do it (I can't find anything in Accessibility to announce incoming calls). There are plenty in the Play store.