How to tell if watch is stolen or fake

If an Apple Watch is stolen it would be under Activation Lock to the user's Apple ID and you shouldn't be able to use it.

Activation Lock -

https://support.apple.com/en-us/HT20144

I don't know how to tell if it's fake. I wouldn't think that a fake  Watch can be paired with an iPhone.

Set up your  Watch -

Set up your Apple Watch - Apple Support

M1 Mac mini, macOS 13.5.2;  Watch, series 7 GPS/cellular, watchOS 10.0.1; iPad Pro 2nd Gen, iPadOS 17.0.1; iPhone 12 Pro, iOS 17.0.1; TV 4th Gen, tvOS 17; HomePods, audioOS 17 and Airport Express w/ Airplay 2