Call information is sent to the receiver if the call is identified by the sending carrier. Some cell carriers do not include the ANI information ( automatic number identification) when it’s a cell to save bandwidth even though it’s small. My cell only shows a name when the number is in the contact list so ATT is saving the data that would be used to send the info. Now for the other issue. Not all cellphones will even read the data packet even if included, most wont. The other possibility is the setup on your contact list that's preventing any display even though you have a name in the contact list. These links are some of the issues blackberry lists so maybe one will help.
KB33685-Caller ID does not show associated contact when country code is included in phone number
KB33603-How to manage which accounts will display in the Contacts application on the BlackBerry Z10 smartphone