How can I use hook_comment_view?
First, PHP is case sensitive - don't start your function names with capital letters, it's bad practice, capitals are generally reserved for Classes.

Secondly, if you haven't already, install the devel module, it's really useful.

Then you can look at the structure of the $comment object that is passed to the hook by putting dpm($comment); inside your hook.  Make sure you give yourself the permission to view devel information.

Once you can see the structure of the variable it should make sense what drupal is doing with it.  You can add a new element to the form simply by editing the $comment variable:

$comment[#myNewElement] = array(
  'property1' =&gt; 'value1',
  'property2' =&gt; 'value2',
  'property3' =&gt; 'value3',
);


You can learn about the various form elements and their properties at the Drupal form API.

You will probably need to query the database to get your display value before you set the element.

Happy coding!