Korean and Chinese names are kind of similar. They're basically always 1 syllable and no longer, and they place them first culturally. First names can be whatever you want beyond that, and there are no middle names.

So Kim Jong-un's first name is Jong-un, last name is Kim. Hu Jintao would be first name Jintao last name Hu. Whether you put a space or dash between syllables when you transliterate to English is 100% a matter of style preference. I can't speak for Korean, but in Chinese each syllable is one character, and there are no spaces between either syllables or different words.

Jong-il being similar to Jong-un is just a choice they made, but they're not numbers or anything. Jong-il's father was named Il-sung.