How do I remove a watch from my device permanently?

See the 'Remove a device from the list' section in:

Check your Apple ID device list to see where you're signed in - Apple Support

To unpair and erase watch and remove Activation Lock.

On a computer, go to iCloud.com and sign in with your Apple ID.

Go to Find Iphone.

Select All Devices, then click your Apple Watch.

Click Erase Apple Watch.

Select Next until the device is erased.

Click the remove button next to your Apple Watch.