Activation Lock prevents unauthorised use of Apple Watch if it is lost or stolen.
The previous owner should have removed the lock before selling their device.
To be able to pair the Apple Watch to your own iPhone, you would need the previous owner (who may not be the seller) to either enter their Apple ID and password on your iPhone or to turn the feature off via https://www.icloud.com/ (by signing in with their Apple ID > Find My iPhone > All Devices, then select the Apple Watch > Erase Apple Watch > Next until erased > click X next to the watch).
If you cannot arrange for the previous owner to do this, then you should, if possible, return the Apple Watch for a refund.
You will not otherwise be able to use the Apple Watch. There is no way around this security feature.
Apple will not advise you of the previous owner's contact details, nor will Apple pass your details on to them.