To enable the feature, head to Settings → Phone → Announce Calls, and then choose when you want a caller’s name to be announced out loud. You can have this happen on all incoming calls, for incoming calls when you’re wearing headphones, or for incoming calls when you’re wearing headphone or in the car.
If you’d rather Siri keep silent — you may be in a public setting and don’t want other people to know who is calling you — choose the Never option so that none of your incoming calls are announced.