Normally when upgraded I am given a new boarding pass with the new seat number printed on it. On one occasion, though, when I was upgraded from Club World to First, staff at the gate simply wrote my new seat number in ink on my existing boarding card. I did wonder whether the cabin crew might think that I'd done this myself in order to obtain an upgrade but figured that the crew would doubtless have a list of all the passengers in First that day and their seat numbers.
P.S. The gate staff did not tell me that I'd been upgraded, simply that my seat had been changed. I could tell instantly, however, from the seat number that I was not travelling in Club World that day!