What is the 'computername (This computer)' domain?
This domain is actually the computer itself. It is a local account ONLY. Desktop users will rarely (if ever) log directly into the machine itself. The only reason that a desktop user might need to log directly into the machine is if they are trying to install a printer or software and need administrator rights. Laptop users, on the other hand will login to this domain exclusively, since they have accounts on their laptops. After logging into the laptop locally, you can run Wake (assuming you are on the network) by double clicking the icon on the desktop, entering your username and password, and clicking Login.