Complex answer: a naming phenomenon exists in Japan, utilising kanji that looks cool, in order to write names that would typically be written a different, more common way.
It is not so strange for parents to want their children to have unique names, nor for manga authors to name their characters using these conventions. It enables them to give their main characters names that are not used in other manga. Ohba-sensei chose the kanji that means moon to represent a new meaning of “light”, stretching the meaning of the original just enough to still be understood.
Why Light Continues to be Called Tsuki Yagami or Raito Yagami by Fans Today
Then - back when Death Note was first released - and now - with each new person picking up the tale - every Japanese reader would assume that Ohba-sensei intended his protagonist to be called Yagami Tsuki. They have no reason not to, until Light himself explains in the manga how to pronounce his name. That doesn't happen until, I believe, chapter twelve.
During his encounter with Naomi Misora, Light goes to great lengths to spell out precisely how his kanji is meant to be read. It seems a little strange in context; too long-winded an explanation over a simple name pronunciation. Particularly in conversation with a lady whom Light is about to kill, concerning kanji that she can't even see written down.
All proving how unusual it is for a Japanese schoolboy to be called Light, spelled as tsuki kanji and pronounced raito. So uncommon and strange that some readers still opt for what the kanji is more obviously telling them, hence all three names continue to be prevalent throughout the fandom and even the rarest of them - Tsuki Yagami - may still be heard.
It may be that Ohba-sensei waited so long before (literally) spelling out how he wanted Light's name to be known, because the author hadn't quite decided the issue for himself.
Not until Death Note 13: How to Read was more insight divulged on the subject. In the interview with Tsugumi Ohba, it's stated that he struggled with Light's name, unable to settle upon the right one. Then his editor suggested 'Yagami' and it sparked enough inspiration in the writer that he went on a quest to find the kanji.
When I looked through the Japanese name registry, I found the Kanji for 'star' and 'light'. At first, I wasn't too concerned about it. But the final scene in the manga gave his name deeper significance. I liked that.
- Tsugumi Ohba, Death Note author, How to Read: Death Note 13, p 61.
The writer had found the right name for Death Note's central character. Now he just needed the manga reading public to switch tracks with him, and that last scene would be beautifully full of symbolism.
Yet he kept the moon there too - in the first pages and penultimate ones too, as evidenced by the twin images shown at the top of this article; in situ bookmarking hundreds of pages across 108 chapters. The Yagami Tsuki people were able to feel validated in stubbornly retaining that original presumed moniker for their character.
But then turn the page and that light upon the worshipper's face could just as easily be cast from a star. At least metaphorically, with the star of hope. There's a nod to the editor's name registry book and the dual meaning of the star-light Kanji found inside. The moment when Ohba-sensei could breathe life into his creation; for no persona lives on the page, until its name is known.
And again, turn a page to the manga's final word - a simple candle and its glow burning bright. No celestial being this, nothing so divine. Just Light, casting shadows, and the nothingness beyond. Great final scene. Good name.
Death Note Names: The Kanji of Light Yagami (Guest Post by Renchan)
Amaryllis's analysis of why Light Yagami may be called Tsuki Yagami by some fandom members, was posted as part of Death Note Month of Kira.
Running throughout February 2016, anyone may contribute Kira related content for this event. That includes you, and your mate.
To find out more about it, visit Death Note Month of... Home; to send in articles, art, recipes, queries, fan-fiction, tutorials, opinion pieces or any other wonders you're moved to share, please visit our sparkly new Month of... Reader Submission Page.
Cosplayers, you now have your very own Death Note costumers' questionnaire, as another option for inclusion in the Month of... focus. Other groups, you'll get one soon, if you're an artist, writer and - if there's demand enough for it - role-player. Nudge us to request more community surveys for any other category of Death Note fan expression not yet counted.
Just want to read more on Death Note's Light Yagami? Lay on, MacDuff.