Would like Siri to only respond on watch and not iPhone.

Hello vernonfrommontville,

Thanks for reaching out in Apple Support Communities. 

We're more than happy to help out today with “Hey Siri” and your devices. It looks like you posted your question from the article Use Siri on your Apple Watch. That’s a good article to use.

You can turn off “Hey Siri” on your iPhone, and use “Hey Siri” on your Apple Watch. To turn off on iPhone, go to Settings > Siri & Search > turn off “Hey Siri”. You can also make sure the settings are correct for your Apple Watch by opening the Watch app > Siri > make sure it’s still enabled here.

Reach back out if you have any questions.

Cheers!