Arduino Bluetooth to Arduino bluetooth

I am using a JY-MCU bluetooth module to send data to a laptop, and this is all OK.

I am contemplating making up another minimal Arduino serving as a bluetooth remote display.

The module has its name, ilfor or something, which is apparently universal to its type, but I would prefer to stick to the module I know. Would having two blueteeth with the same name be a problem? If so, is it possible to change the name?
I have never sent commands to bluetooth. I just suck data.

Gee, that fell on stony ground............

I take it this is not such a good idea then?

I was trying to avoid other sorts of wireless communication.