FileMaker passwords are not specific to a given computer so you should not need to change a FileMaker password on any one computer. From any computer that can access the DB, you would need to log in with a full access password in order to change a password unless the developer created a system using scripts that can manage (non full access) accounts/passwords on the system.
I am able to sign on using my name/user name and my password. I want to change my password.
I do not know where to go to change my password.
If your access privileges do not allow it, you cannot change your password.
If they allow it, you would use Manage | Security to change your password. Make a copy of your file first to make sure that a mistake on your part does not lock you out of the database. If this is a hosted file, you might first try this on a back up copy before doing so on the currently hosted copy.