I can't remember the exact context, but on an older podcast Jeff mentions saying different site names over and over again to find one that did not sound dumb no matter how many times he said it. So unless i am completley mistaken it has no real context. It's not named after anyone or anything or any event. Its just a name that sounded good at the time.
I think there's probably an element, especially early on, of Jeff and co. being considered somewhat explosive in the media space following the GameSpot events and trying to build a brand off the back of that.
There's this great screenshot of a whiteboard with Jeff's ramblings about what the "bomb" art should look like in an episode of How to Build a Bomb. Ancient video at this point, but I have the screenshot for some reason:
"Bomb should have a face, but not really a mean one. This bomb isn't angry about being destructive. It's totally excited. It was born to blow up, it's totally going to blow up, and it couldn't be any frickin' happier about it. But maybe there's a hint of mischief in there as well?"
Some insight into the name Giant Bomb there, maybe.
I remember Jeff or Ryan saying, Bomb as in something big and spectacular like "This is the bomb"; or if everything went tits-up teh whole thing was a giant bomb as in, "to be or make a complete failure, especially to fail to please or gain an audience" It was going to be either one of those 'great success or horrible failure'.
I feel like I remember a video where the crew explained it a long time ago. Something about during the idea phase for the site someone (or everyone) joking about how ambitious the site and going on their own was and it was going to be a giant bomb, so they made that the name. For some reason I also associate the memory of Dave making breakfast or something and it being explained around that time that they announced giant bomb being sold to CBS. It's so long ago though that I could just be filling in memory where there isn't any.