How many LED displays can be hooked to one Arduino board?
The led displays will be pretty far out from each other.


Those are I2C connected displays. I2C is not designed (though there are technologies to allow it) to operate over long distances. It's designed primarily for communication between chips within a circuit board.


  How can i uniquely identify the LCD displays?


Since you can't change the I2C address of the displays you would either need a separate I2C bus for each one or employ some form of I2C multiplexer.

All of this is getting too complicated. The more accepted way of doing this would be to have a small microcontroller directly connected to each display (one display per microcontroller) and then make the microcontrollers communicate with each other (or with a single master) over some suitable communication medium (some wireless system, or a serial bus like RS485 or CAN, for example).

You're then just rubber-stamping the units as many times as you want, and connecting them all together.