A schoolboys' Latin (i.e. poorly grammatical) phrase meaning "good voice," "Bono Vox" is a nickname that was given to Paul David Hewson, lead singer of the Irish rock band U2, by a high school friend dubbed "Guggi" (who later became a vocalist for the Virgin Prunes) when they were members of a social group called "Lypton Village." The nickname has been shortened to "Bono" for all intents and purposes, and is pronounced with the same "bon" sound in "bonbon" (if you pronounce it "BONE-oh," you are referring, voluntarily or not, to Sonny Bono of Sonny and Cher fame).
There are varying accounts of the origin of the name, but one source asserts that Guggi found the phrase "Bono Vox" in a hearing aid store in Dublin's O'Connell Street that sold "Bonavox" hearing aids. In any case, given that Bono's first Lypton Village nickname was reportedly "Steinhegvanhuysenolegbangbangbangbang," I think that U2 fans and the media dodged a bullet with this one.