Do you even have to tell them? The device is so new that ALL of them are still under warranty.
When filing a claim, do they ask for proof of purchase? I bought mine a month and a half ago and will be calling them tomorrow because it mine has a cracked (2 cracks) back.
I am not sure about the Moto 360, but when I filed my claim for my Moto X front camera they asked for the order number.
Another thing to note is that when I purchased the extended protection plan for both my 360 and my X they said that it was transferable if I sold either device.