Remove E-mail and URL field from Comment Form

If you would like to remove e-mail and URL field from comment form, first uncheck the requirement in Settings > Discussion:

Then add the PHP snippet below to remove the field

add_action( 'after_setup_theme', 'tu_add_comment_url_filter' );
function tu_add_comment_url_filter() {
    add_filter( 'comment_form_default_fields', 'tu_disable_comment_url', 20 );
}

function tu_disable_comment_url($fields) {
    unset($fields['url']);
    unset($fields['email']);
    return $fields;
}