If I get the same wireless computer for my girlfriend, will that mess up both of ours when we are riding with each other?

Cateye CC-MC100W Micro Wireless that is what I have, and would like to get her one.

We have three of them in our family, and they've never interfered with each other.

Neon lights, on the other hand, make them go nuts...

I guess it shouldn't. I went through the user manual using the link above but couldn't see any way of pairing the computer with the sensor. Which makes me wonder if there is any coded pairing mechanism at all. Best would be to ask the salesman at your LBS to verify.

the typical range of the wireless is between 60-80 cm, that's under a yard, the wireless won't affect each other. I have a Bell wireless as does my riding buddy, and we never get any interference.
but as mulveyr mentioned, if you have a higher power light with a blinking mode, the blinking does generate interference thatt's picked up by most wireless bike computers.

I have picked up Min if i have my bike computer next to my Netbook, but not any miles, I have a SSD so i dont know what its picking up,

I uses a Light and Motion Stella 200 and have never noticed any interference but i have never really looked at night to much at my speed.

I used to use a Cateye 7 wireless, until I tried riding at night with my Niterider MOAB HID headlight. The light caused the computer to completely shut down.

I always go wired. I don't see a big advantage to going wireless. They don't seem as reliable as wired ones.