If you own a 1st generation Automatic adapter, Automatic will not appear in the “My Devices” list in the Bluetooth menu until you've gone through Setup, and it only appears in the Bluetooth menu when your phone is connected to the adapter. Setup occurs in the Automatic app so be sure to go there to get started. You don't pair the adapter from the phone Settings menu.
If you own a 2nd generation Automatic adapter, the adapter appears in the “Devices” list as soon as Bluetooth detects it, and it will appear as “XX-Automatic Adapter” (with XX being the first two digits of your adapter’s PIN). See this FAQ to read more about going through setup on a 2nd generation Automatic adapter.