First thing is are you really setting up your new iPhone with a new Apple ID You will lose all your Apple iCloud assets including purchases, photos, and calendar etc.
Either way you need to gain access to your old Apple ID and password because you will need that combination to free off the Watch in https://icloud.com/find .
Try the steps in this knowledge base article
in order to find your apple ID
https://iforgot.apple.com/appleid
Try the steps in this knowledge base article if you forgot your Apple ID Password
If you forgot your Apple ID password - Apple Support
or look in https://al-support.apple.com/#/getsupport
Further information can be found here About Activation Lock on your Apple Watch - Apple Support
Of course if this is a foundling Watch or an unwise purchase and the apple ID in question was never yours then you cannot free off the Watch