Change Default Organization
You should be able to set it in Administer > Communications > Organization Address and Contact Info, as per: Wrong default organisation

ETA: As I just went through the process of transferring to a new server, I've realised that the instructions result in your original civicrm_domain being skipped in the MySQL dump. A fresh install of CiviCRM on the new server will assign the contact id 1 to the default organisation in the civicrm_domain table - you can get around his by either including civicrm_domain in the initial SQL dump, or by editing the contact_id field in the new database's civicrm_domain table.