I am sorry that the proposed solution does not solve your issue, I have misunderstood this part
And this part:
As it sound like there is already the customer in Zammad
So, if I got that right now, the external company receives a case ticket from customer that can be one to one million and always different and your company solve the case for the customer and not for the company?
And the email has the details in the email text and the customer already in Zammad?
Or how does that process look like exactly?
Now sure if Zammad supports that out of the box.
Zammad could read the customer name from the email content and set the customer.
With Triggers that would mean up to a million triggers, which does not make a lot of sense.
Eventually you might need to build your own middleware solution and use the Zammad APIs to associate the customer with data from the email data depending on the information you get from the telephone company.
But with limited insight in the whole process it is hard to tell.