The Apple Watch will be using the same Apple ID as the iPhone to which it was last paired - in this case probably your previous iPhone. Did you setup the new phone on the same Apple ID as your previous iPhone? If yes then you already have the details you need.
If you used a different Apple ID for your new iPhone and your old phone is still usable (although retired) you might be able to get into the Apple ID account and release the Apple Watch.
If you forgot your Apple ID password - Apple Support
If you are unable to recover the Apple ID login credentials and release from the old ID your watch will be unusable.