I'm not a lawyer but I don't believe it is as clear cut as you believe. Music copyright is far tougher than literature.
Example 1. Your character's name is Jack. He owns a convenience store on the edge of town. He is a suspected paedophile. One day he is found dead in his store.
- You could well be in trouble. Not only are there too many coincidences but you've 'damaged' another work. (Google: 'Grocer Jack').
Example 2. Your character's name is Norma Jean. It is revealed the character does not know who her father is but her mother has admitted she was conceived in the woods after an Elton John concert.
- This is okay for two reasons: you have stated that your character is not the subject of the song. (2) "Norma Jean" is a real person who could be defined as a celebrity. (Google:"Candle in the wind."
Example 3. Your character's name is 'Lucy' or 'Alice'. She is attracted by the glamour of the music industry. In the end she is unable to cope with the culture and dies from an LSD overdose.
- You're in trouble. Your entire story is a rip-off of Beatles song.