Your personal or business name appears above the number of the person receiving your call. The record with the information required to display your caller ID is not forwarded automatically to your new provider, though some providers do perform this service automatically.
If your service provider and carrier are different companies, you need to check with the outside carrier in order to ensure that your caller ID is activated. Some service providers do this for you and some require that you call and request this to be done, sometimes for a small fee.
This is why it’s important to inform your carrier of any personal or company name changes if you want your caller ID to reflect the new information. Only some providers will update this for you automatically, without your verbal request.