add a "will not be published" field on comment form

Hey everyone

I would like to add a custom field to the comments section on my blog posts.

I want to capture people’s phone number but not publish it – exactly the same as with the email field.

I’ve looked everywhere for a plugin or some code help – but I think I’ve discovered a feature that’s not been added before! In other words, there’s nothing to be found on this subject!

I’m happy to code the comments.php file – but what I am missing is what to add to the functions.php file in order to communicate with the DB ?

function my_fields($fields) {
$fields['new'] = '<p>Phone Number (Optional. Will not be published)</p>';
return $fields;
}
add_filter('comment_form_default_fields','my_fields');

I would really appreciate any tips!
Thanks