Only through BellSouth really. The reason is that in order to pass Caller ID name data, Bellsouth (and other landline phone companies, for that matter) must either subscribe to a third party database that can cross reference phone numebrs to their subscriber names, OR directly negotiate with the various carriers to pass the name information. Generally, a telecom company (wireless or wireline) will charge a fee per name that is passed along, while the number-only information is free.
What frequently happens is that a wireline phone company will decide they are paying too much for this service (prices typically run $.02 to $.04 per name accessed), and refuse to sign a new contract until the originating carrier is willing to negotiate a lower price. The idea is that the wireline company beleives they can strong-arm the other carrier; if caller id for that carrier is "broken," then they believe that customers will not want to subscribe to that competing phone company.
So in essence, you are right in contacting BellSouth. They have made a decision not to provide accompanying name data, beacause they don't want to pay other phone companies for the privelege (yet they're probably quite happy to charge others for the same info).
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