"Luz" is an incredibly common name in Spanish speaking countries. It means light. "Luce" means light in Italian, but seems to be less common as a name. Lucifer means "Light-bringer", and the myth of the light-bringer is much, much older than Christianity.

Old religions thought things in the sky were gods. Venus orbits closer to the sun than the Earth, which means light reflecting from it is extremely bright, but that light is only visible near sunrise and sunset. During the rest of the day the brightness of the sun overwhelms the reflected light from Venus, and during the rest of the night it's not visible because it's near the sun, so it's behind the earth. So, old religions talked about the brightest "god" in the sky, who disappeared when it got too bright or too dark. That led to the myth of the god who tried to be the brightest light and was cast down. That, of course, led to Satan, A.K.A. Lucifer.

I guess the Catholic church was giving its followers too much credit in their understanding of words.