Boy oh boy, I have a love/hate relationship with silly names...
As a DM I'm pretty strict about silly names, if I have any intention of the keeping the game going. On the other hand, I am one of those players that will come up with an in-depth character concept, as many pages of back-story as the DM cares to ask for, and hand-drawn illustration of a character, but my brain shuts down when I try to come up with a name.
My first D&D character ever: an elven fighter called Xerocks. Because I had a bunch of photocopied character sheets in front of me when I tried to come up with a name. Hey, I was in third grade, gimme a break, okay?
The gaming group I'm in now has had some doozies. Otherwise a pretty mature group, the running threat is that if a character doesn't have a name in the first half-hour of the game, he'll be stuck with "Slinky-head". This threat has only been carried out once, to my knowledge.
There was also a Champions character who, out of pride, refused to give himself a name. He was a young samurai, and such silliness as superhero names was beneath him. The DM, after giving him fair warning, had the news media dub his character "Kid Ninja". The campaign went on for years, and all the time the poor guy had to explain to everyone "I'm a samurai, not a ninja, dammit".
A con artist character of mine had to come up with an impressive sounding name on the fly, as part of a bluff roll that I totally botched. On a moment's notice, the best/worst I could come up with was "Count Gustav Von Umlaut". I was pretty proud of that one.
The list could go on, but I'll spare you...