How do I replace part of a webform component label with a variable token?
hook_form_alter() should allow you to so.  

Within your theme you should be able to do something like :

/*
 * Implementation of hook_form_alter()
 */
function my_theme_form_alter(&amp;$form, &amp;$form_state, $form_id){
  // target my form / my field
  if ($form_id == "my_form") {
    if ( $form['my_field']['#title'] ) {
      $title =  $form['my_field']['#title'];
      $token_val = get_tokenised_value(); // Which ever way you handle that...
      $title = str_replace('[your pet]', $token_val, $title);
      $form['my_field']['#title'] = $title;
    }
  }
}


Also check the forms api reference to see what things you can set / alter on forms.