How are CiviCRM form names defined (civicrm_validateForm)?
In principle the names are based on the files, so the form which is CRM/Contact/Form/Contact.php will be CRM_Contact_Form_Contact.

AFAIK the name of the form will always be commented if you inspect the form with Firebug, Firefox or Chrome.

In some cases forms will be called from pages (like the contribution page). This is kinda hard to find out, I always do a post hook in my extensions to log the $formName parameter to find out what forms are called during the process.

AFAIK you will need to include a call to the form hook to make sure your customized form is also usable in a validateForm hook (see below). But I would certainly try first if the parent CRM_Core_Form does not handle that and you can indeed already check for your customized form name.

    CRM_Utils_Hook::validateForm(
  get_class($this),
  $this-&gt;_submitValues,
  $this-&gt;_submitFiles,
  $this,
  $hookErrors
);