Hi Rocketman3,
If you will be diving close together, I recommend having 1 gray and 1 yellow. As THX723 mentioned, each and every transmitter has a unique code so you would never have a situation where your Perdix would erroneously show your wife's information.
However, the reason for the multiple colors is slightly different than this. The different colors have different transmit periods. For example, a gray might transmit every 5 seconds, but a yellow every 4.9 seconds (these aren't exact numbers). The reason they do this is that it is hard for the receiver to reliably receive two communications at the exact same time. A communication burst only lasts about 0.1 seconds. Normally, even with two gray transmitters the communications happen at different times, and there is no problem. But if two gray transmitters ever randomly end up synchronized, their transmissions will collide and both receivers might drop out. The transmitter clocks are very accurate, so it can take a while for 2 gray transmitters to drift back out of sync (typically a few minutes up to 30 minutes, depending on how closely matched the transmitter clocks are). With the different colors, the transmit periods will never end up synchronized. Collisions can still happen, but they would quickly move out of sync.
I hope this explains the reason for the multiple colors. So it is safest to have 2 different colors if diving closely together. However, you can still usually get away with 2 gray transmitters. If the transmitters are different distances from the receiver, the stronger signal will typically win.
Best regards,
Tyler Coen
Shearwater Research