Having reviewed the code, the printer template tag {USER NAME} only finds the name of the user who created the ticket in question.
I managed to edit the code, so now I have three printer template tags including {USER PAID} - user who logged on when taking current payment, and {USER LOGGEDON} - user who is currently logged on when printing any template.
So now I can track who printed the bill, who took the money and the dates and times by printing this information at the bottom of the printouts