I think it was this Rolling Stone article that explained where the White Stripes got their name. When trying to conceive that unique Jack White-Meg White sound, the two decided that one common, everyday object best represented their goal: those round, red and white after-dinner mints you get at restaurants. Simple. Classic. Beloved. But not knowing the name, they simply called them — and, thus, themselves — the White Stripes. Appropriate, really. The candies jelled with the barebones rock aesthetic and the two ran with it.
A funny story: I'm at the grocery store looking at the bags of Bracch's candy. You know, the nasty, chalky stuff parents hand out at birthday parties after the kids are sufficiently rattled with the good sugar. But those same red and white candies, according to the Bracch's company, are called the Starlight Mints, a name shared by a lesser known but also wonderful indie rock band.
Two bands, one candy and essentially the same name.