A more detailed explaination and breakdown of Light's name:

Japanese kanji: 夜神月
English: Yagami Light

But because the Japanese hiragana do not have sounds started with L the closest is R, thus his name is pronounced as Raito, using the hiragana らい for "Rai", and と for "to". As long as official names go, it's Yagami Light, or Light Yagami if you want the surname to go last.

And remember Misa reading his name wrongly when she first saw him? That's because the character 月 is usually pronounced as "tsuki", which means the moon. In Light's case, it is pronounced differently, and is based on the english word "Light". This is why Misa commented on how unique Light's name was.

Hope this clears up any confusion.