Caller ID is a network setting.
Details of how to change it depends on the phone you have and the version of Android it is running, however on vanilla 4.3 go to the dialer and hit:
Menu
Settings
Additional Settings
The phone will then contact the network to download the settings. The first option is Caller ID. Tap this to disable.
If you can't find the setting, call your network and ask them to disable it for you.
Note that once you do this, you will not be able to see the incoming phone number.
If you mean that the phone is reading out the name, then that's a feature of your phone so you will need to re-post with details of the phone manufacturer, model and the version of Android you're running.
