What type of security/log-in model are you using? Is it Access MDW or standard network log-in ID? or some home-grown system you designed with VBA?
If either of the 1st two, then you can grab the userID by calling either of two variables, depending on which system you are using. Otherwise, you will have to keep some form open all the time, or declare/use a global variable in a VBA module. My choice would be to store the variable in the Switchboard form in a public variable, rather than use a globa variable in an outside module. If you ever need to "close" the switchboard, then you can switch the form to visible = false rather than close it out.
Also, I'm not sure if I understand you correctly, but going by how you worded what you said, it appears you are counting on the end-user to close out of the switchboard form and trigger the Exit function to log-out. I would switch the "log-out" tracking function to the On_Close event of the switchboard, so that even if the user clicks the X in the top-right corner of the screen, the tracking function still fires.