Any advice I give is purely speculative, but if I were trying to hide my identity from blizz.
IP
If you use a static ip change it or if you plan to regularily abuse the economy use a tunnel.
If you use a dynamic ip, a simple ipconfig /flushdns should suffice
MAC
The most obvious part of your hardware they can see is your network card (I think, please correct me if wrong). Each component has a unique ID. The way I understand it is, the combination of your hardware IDs is a way to identify your computer. Change one! Though it is more troublesome, if I wanted not to be identified, I'd change the motherboard.
Format
Not really essensial, but is good practice if changing the mother board. Blizz are not legally allowd to scan your computer for personal info. This includes software currently running, personal documents/projects/software, browser history, etc.
Payment
This on is a no brainer. 20 accounts bought with the same credit card running on the same pc(s), ip, following similar login/logout patterns is a bit of a give away.