It's one of those things you probably never bothered to think about. "GameStop" sounds like something it took three seconds to come up with. But there's surprisingly a bit more of a story behind the name.
Executive Chairman of the company (and also founder and former CEO) Dan DeMatteo has told Reuters that he named the company after an old franchise of...book stores.
Bookstop was the name of a chain of stores in Texas and Florida specialising in not the trading in and sale of used books, but in discount books. You know, the type that spring up in empty mall spaces to sell excess stock. In 1989 it was bought by Barnes & Noble, taking the name off the market, and DeMatteo had his inspiration.
GameStop, once known as Babbages, was first founded in Texas, hence DeMatteo's familiarity with BookStop. He's used it again for MovieStop, a spin-off line of DVD stores.
Just goes to show, even the most mundane and obvious names for things can often have a slightly more interesting story behind them.