Somewhere I read that those who develop mods for vbulletin can not use "vb" to prefix their mod name without permission. Is that correct? if so, are there any requirements? How would be go about asking permission and who would we ask?
It's reserved for official vBulletin products made by Jelsoft. You can't get permission unless you work for Jelsoft and are creating an official vBulletin product.
You can use "vb" in the name, however, it should not be used as the modification identifier.
I'm not sure what you mean by "modification identifier". If I understand what you mean is that I can use "vb" as a prefix to the name of my mod, for example if I was making a game for vbulletin, something like Othello or Chess.. I could call it vbOthello, or vbChess? Correct?