Personally I don't like puns, due to a devotion to Straight, however, I confess I use them from time to time in Classic to Zap games. I could also use puns in Straight, if the NPCs are purposely punning, and not the GM.
For example, there is a hot new vidshow called "CSI: CSI Sector". A pun on CSI, yes? But, Troubleshooters will slowly finds out that the vidshow is actually funded and created by the Romantics society. The Romantics Society knows about CSI, and wants to bring it back to the world. It decides the best way to do it is to just copy the entire show, and even use the same name, basically making a pun that only they would "get".
Another example is prehaps the pun name of Robb-Y-BOT is purposely punny, but does not actually exist. Rather it is just a codename used by Corpore Metal agents, and the man who is hiding under the Robb-Y name may be anyone, from a common INFRARED to an ULTRAVIOLET, or even a warbot.
Hey, can't people living in Alpha Complex have humor too? Especially bad humor? I could see Mystics cracking up very, very bad pun-names during their freak-outs, just to try and elict a laugh from their fellow society members. Computer Phreaks can hack into the compnodes and come up with false idenities like BLUEs and INDIGOs, people that don't actually exist but just data so that the Phreaks can further their contorl over FC, and I suppose they can decide to play around with puns themselves, creating false accounts like Tray-I-TOR, so they can laugh silently at their pun.
Hopefully, Troubleshooters, if they encounter such a strange situation, will notice these events and stop these traitors I listed above.