This is interesting. Despite having been to Los Angeles three times to visit relatives there, I never bothered to ask about this. I was thinking that "angels" is referring to the people of Los Angeles. But guess the name was given in recognition of St. Mary who was know as the "Lady of Angels" or "Queen of Angels."
It's kind of ironic now because there is a lot of crime in Los Angeles from what I know. My brother and his wife live there and they're always complaining about the crime. Plus, Los Angeles is also the city that never sleeps. There is a lot of night life and there are a lot of people there so crime is bound to happen.
Oh and there is also a Red Hot Chili Peppers song: City of Angels. I actually love that song.