I've been writing an autobiography about sexual abuse that happened to me throughout my childhood. The abuser was the dad of a famous singer. Once I was old enough (18) to leave home and file charges (I carried the abuse in silence as a child), my singer relative had become very popular. I didn't want to ruin his fame. Fast FWD 35+ years...the abuser is dead, the singer is still around, and I have a need to write this book without biting my tongue anymore. My story will not be about this singer, but yet feel it's important to mention the reason for me keeping silent all these years. I by no means am accusing them of any abuse or knowledge of it. Is it legal to mention the singers name? I'd also like to use one of their song titles as a subtitle. Is that legal?
Merely mentioning the name of a famous singer and songs that the singer has written does not violate any intellectual property right of any kind.
That's a no on the song title as subtitle issue too. There is no copyrights on words or titles, but rather the ideas of the work itself. If you are doing this because you know the singer personally, and the song is a more well known song from the singer's career, it's perfectly fine as the whole idea behind the words is being fundamentally transformed and thus Fair Use can be applied. As a sort of example, there are two movies with the title of Frozen... though the first one was nowhere near as popular as the second one (and I'm just now thinking that as the second one is a popular musical... it may be too close... but I don't think anyone in that movie is that old).
Since you are close to this singer, have you asked them if it is alright to do this? Do they know about the abuse or will they be put on the spot when this is released.