Caller ID Display on Recipient's Phone

I have two issues with the my caller ID information displayed on the phones of people I call.  When I make calls from my home (cox) phone, the caller sees only my number and not my name.  I want the caller ID display on the other end to show my name and phone number.  Also, when I reply through the cox voice mail prompt to callers who have left voice mail (call the party back) the other party sees Unknown Caller and Unknown number on their phone instead of my caller ID information.  Is there some setting on my end to correct these issues, or is this something that cox has to address?