Is this Bluetooth module cool for Arduino?
From skimming that post, I believe that your linked pcb is not a full bluetooth module (note how there is no bluetooth chip or antenna of any kind). This is simply a "base board," which is why it is so cheap1.

You will need something like this that actually has the components you want.

To answer your questions:


The bluetooth library for arduino sets the discoverale name to ARDUINOBT by default, but that can be changed in the setup() method.  
"scan around" is a little ambiguous—AFAIK, bluetooth can only connect to one device at a time, but I'm not sure if that's totally true. You may want to look into using radios instead of BT, as they can communicate more freely with one another, are extremely cheap, and have extensive arduino libraries availible. I'm currently working on a project that uses the nRF24L01, and I'd be happy to answer any questions you have about it.


1: It also has a draw of 6v VCC, which is more than the Uno can output.