sms forwarding - remove old device and add new device

Hi there,

Apple Tech has not been able to help me solve this problem. I recently got a new Macbook Pro. I sent my old Macbook Air in as a trade in. My iPhone still lists my old Macbook Air as the only option for SMS forwarding. Sometimes that option totally disappears in the iPhone messages settings menu, but when it does show up it only shows my Macbook Air. Does anyone know a) how to remove my old Macbook, b) how to add my new Macbook, and c) why it sometimes disappears? thanks!