Does your Caller ID never show a name or number, or does it only fail to show specific names or numbers?
If nothing shows, then you should contact your carrier, since Caller ID is controlled by the carrier.
If only certain names or numbers do not appear in your Caller ID, then those particular callers may be blocking Caller ID on their end. There are settings to block or ignore unknown numbers. Which Moto phone do you have? What carrier do you use?