("new" is the user that the script runs as, "old" is what the user originally logged in as)

¹ as determined by running who am i or logname

• who internally uses ttyname() to find the tty associated with stdin, after which you can easily find the owner of that tty
• logname internally uses getlogin() to find the login associated with the controlling terminal
• see more here

² This data is unavailable if there's no TTY (for instance, when running under 'cron' or under a web server)

³ unless stay_setuid is specified in /etc/sudoers