how to display the machine name of module at /admin/modules?
If you don't mind going low-tech you can just look at the value of the checkbox next to each module; it contains a string like:

modules[Core][aggregator][enable]


In that example, aggregator being the machine name of the module.

If you don't want to go low-tech you'll need to implement hook_form_alter(), loop through the module data in the form and add the machine name somewhere.

For example, the following code will add the machine name in brackets after the title of each module:

function MYMODULE_form_system_modules_alter(&amp;$form, &amp;$form_state, $form_id) {
  foreach (element_children($form['modules']) as $group_key) {
    foreach (element_children($form['modules'][$group_key]) as $module_key) {
      $machine_name = " ($module_key)";
      $form['modules'][$group_key][$module_key]['name']['#markup'] = $form['modules'][$group_key][$module_key]['name']['#markup'] . $machine_name;
    }
  }
}


Screenshot of the results on a blank Drupal installation: