Hello Rostislav.
In order to pull up a company, it is necessary that the client of the process be a contact of an individual, who will have the company registered in the card.
Then, when creating a TTN, the full name of this contact
http://i.imgur.com/QcEPByh.png will be pulled up in the field "Contact person", and in the field "Organization or full name"
http://i.imgur.com/beBuAe9.png will be pulled up the company of this contact.