I am writing a book, and I'm trying to figure out how to reveal the main character's identity. It is a crime book set in modern day and is a story told in the perspective of a serial killer. I plan for the reveal to come somewhat early in the book and display the main character's thoughts and mental process throughout the story. I have to get the story out by April 1rst to be a part of a book collection based on inspired songs by the band, Talking Heads. This will be inspired from the song, Psycho Killer.
Have the character talk to themselves
"Oh, what have you gotten yourself into John", I asked myself. I'd worked in marketing for years, but had no clue how to spin this. The blood would wash off, but getting an alibi was harder.
Or have someone talk to the character
Peter called out to me, "Hey John, what are you up to?" I didn't really want to talk to him, but couldn't find an excuse. "Hey Peter. Not much, just killing random people. Haha." Peter laughed. I was such a kidder.
Or have the character read something referring to themselves
I looked at my business card, "John Doe, marketing director." The graphic design was awful. Whoever designed that was going on the list. It was probably Peter. The only reason I hired him was because he married my sister.
Just have the POV character be introduced to a new person by a mutual acquaintance, they have a short exchange ("what do you do?" kind of stuff), then fairly quickly, the POV serial killer traps and kills that new person they just met. Perhaps it was part of their plan to meet them socially, so the victim would let their guard down.
Perhaps the POV character picked up the victim in a bar, something like that.
In a First Person narration, the character is the narrator, and hence can say anything they want to say, directly to the audience.
In fact, everything is addressed to the audience. Although, the "audience" to which the story is directed may or may not be your reader. Digressions into any set of side details could be the rambling of a crazy person, or could be clever tie-ins showing off the character's intricate intellect.
The question is not how to reveal information, but why.
If a murderer is writing anonymously, filling in details of his crimes that might not fully have been appreciated, mocking the police who have failed to catch him, then it would be difficult to justify revealing the character's name, or other personal details. (Unless he's supremely arrogant - "My name Johann Fiddle, and I grew up on [X] St of [Y]ville... But you still don't know enough to catch me!")
On the other hand, if the character is boasting to a soon-to-be victim, any information is on the table. Dead men tell no tales. ("Yes, I engraved my name on the knives I use to kill my victims. Don't worry, you'll got as close a look as you like soon enough. Closer, probably, then you'd like.")
An unhappy confession would have a different flavor, but might naturally include an early self-identification. ("My mother, Janine Fiddle, was a neglectful parent. Not neglectful enough, I'm afraid, because I lived through my childhood to become the monster that I am...")
Based on the topic and main character, this might be a good premise for a nameless protagonist. He might tell his victims variations on a made-up name.
They might be someone whose 'ordinariness' in appearance or disposition makes them un-remarkable – which is maybe the fascination of serial killers? They could be anybody.
If he lies to his victims, we'd meet him again and again as he improvises and learns – the persona becoming more confidant as more details are woven into his 'story'.
Ted Bundy pretended to be a cop, to need help carrying books, to be taking interviews with a tape recorder, etc. Many of his intended victims walked away because his stories didn't add up.