I've sent an account refresh. This wouldn't interrupt the TV signal, but can address the TV Caller ID banner that hasn't appeared on your TV screen. If the Banner doesn't appear when receiving calls, please continue to the website instructions below.
http://bit.ly/2jX68HD is a bitly link to our website with step instructions to access the menu and turn the Caller ID Banner off/on. You will find the steps under 'Advanced TV - Motorola' to fit the steps associated with your Set-Top-Box (STB).
Just a suggestion, but have you tried removing and the re-adding the occurrence to the cable box? Many times the box needs to be updated with how it gets caller ID info from Cox. If so, then I agree the next step would be to check the Cox phone switch to see if the caller ID flag is set for the OP's phone number.