In our company used to work a 'mister X'. He doesn't work here anymore. His computer is now used by 'mister Y'. When opening a database in FileMaker Pro the Account Name is still set to 'Mister X'. Is there a way to change this to 'Mister Y'.
You could be referring to User Name or Account Name. User name and account name are similar terms used to describe different things in Filemaker. I would guess from your question that you are most likely referring to the user name.
To change the user name on mister y's computer, open Filemaker Pro, go to Edit -> Preferences and in the General tab there is a place where you can change the user name.