My neighbor keeps connecting to my Audioengine device; is there any way to add a passcode or extra security to connect via Bluetooth?

There wouldn’t be a way to add any extra security to the bluetooth receiver.  The only ways to prevent a device from connecting to it would be for it to be off, or for it to be connected to your device already; it’s worth noting that only one device may connect at a time.  If a device that you don’t want to be connected is connected to it, you can hold the pair button for a few seconds and it will disconnect from that device, allowing you to re-connect to it.