Different Apple ID for Apple Watch

Activation Lock is designed to prevent anyone else from using an Apple Watch if it's ever lost or stolen.

About Activation Lock on your Apple Watch - Apple Support

Activation Lock is an anti-theft feature that cannot be bypassed. Only the previous owner can remove the lock by using their Apple ID & password. Apple will not help you find the previous owner. If the previous owner cannot or will not remove the lock, then the watch is useless to you or anyone else. Try to get a refund (through eBay) or dispose of the watch properly. In the future, see the 'Before you buy a watch from a third-party' section in:

What to do before you sell, give away, or trade in your Apple Watch, or buy one from someone else - Apple Support

If you are the ORIGINAL owner, then see the 'Start a support request' section in:

How to remove Activation Lock - Apple Support

Here are two ways to unpair your watch if you no longer have the paired iPhone:

• See the 'How to erase your Apple Watch if you don't have your iPhone' section of:

Unpair and erase your Apple Watch - Apple Support

• With a web browser, go to: https://www.iCloud.com and sign in with your Apple ID. Open Find My iPhone and select All Devices (at the top). Then click your Apple Watch, select 'Erase Apple Watch', and select Next until the device is erased. Finally click "X" next to remove your Apple Watch.

You can ask apple to remove the activation lock online on this page;

Remove the Activation Lock Here.

Or this;

If you can't remember/gain access to the apple id that paired the watch to the phone.Take the watch and it's receipt with the serial number along with some photo id and any other proof of ownership to an Apple Store and request that they remove the Activation Lock for you.