The problem causing no one's answering: since not everyone got his surface and a even smaller percentage uses a bt-device on it, the possibility to have your device and test this successfully is rather tiny.
Additionaly your request didn't included any information on the exact logitech-model or what you have tried so far.
But back to trying to help you:
- Got anything paired with your surface so far?
- Headset is working with other devices/you know how to pair this?
- If Bluetooth: Does the surface support the bt-protocolls the headset is using?
- Sometimes moving the objects (at least 1m space between) could help for recognizing.
- If not Bluetooth: Logitech wireless devices often use the unify-usb-transmitter, using some "proprietary" protocoll - got that working?