You can retrieve a ton of information from the device where the workbook is being opened. You could get processor, bios, OS, version of programs, etc., using WMI. There are 1248 classes where you can retrieve meaningful data about the device, and each class has a bunch of stuff to retrieve data from. In fact, many programs utilize that information to create a "device fingerprint" that should let you know exactly from which device the file was open.
But if you want meaningful names, you can have a login form and check against that.
I would also recommend not writing to the same workbook. I would write to another workbook or an external file. In fact, you could log several types of interactions that you define.