How to change "Your name" label in comments form? I have a blog with comments and I need to change the "Your name" field to something different and make it a required field.

Can I do this from hook_form_comment_form_alter() hook in template.php or in a comments template?
You can do it in a hook_form_alter() function like you suggest:

function MYMODULE_form_comment_form_alter(&amp;$form, &amp;$form_state, $form_id) {
  $label = t('New label');
  if (isset($form['author']['_author'])) {
    $form['author']['_author']['#title'] = $label;
  }
  else {
    $form['author']['name']['#title'] = $label;
  }
}