If your database requires logon, you can use the CurrentUser() function to retrieve the name the user logged on to Access with. You can just assign this value to an invisible control bound to the table field in which you want to store it. (Do this in the Form_BeforeUpdate event procedure.)
If your database doesn't require logon, CurrentUser() will return "Admin", which isn't very helpful. In this case you might be able to retrieve the name by which the user logged on to the network, using a Windows API call, but whether you can and how you do it depends on what kind of network software you're running. And I don't have any knowledge in that area. Rick Sprague