If you want there Windows login name use this:
UserName= (Request.ServerVariables("LOGON_USER"
This will give you DomainName/LoginName
If you want there actual name you'll need to register the active directory services interface dll on your web server. You can download it from Microsoft if it isn't already registered.
Then you can get there name using this:
UserName= Replace(Request.ServerVariables("LOGON_USER"

,"\","/"

set User = GetObject("WinNT://" & UserName)
strmyfullName = User.FullName
strmyfullName will now contain (example) "Smith, John"