The following Latinized transcriptions - Zhan Zhengxi, Zhan Zheng Xi, and Zhan Xixi - are all Latin-based, specifically Pinyin-based, transcriptions of the original Chinese characters.
The Zhan surname may refer to: 展, 湛, 詹, 占, or 战/戰. They are all converted into Zhan in Pinyin. Without reading the original Chinese, it is impossible to know which logogram is the character's real surname. Same goes for the given name. Chinese is a tonal language, and the tone can help with logogram identification. But even then, it is a wild guess . . . unless someone reads the original Chinese.
The character's real name may be 展正喜. 正 is a fitting name for a boy. It is used in Kim Jong-un's Hanja name. 喜 makes sense for a boy; a boy gives pleasure to his family. In Pinyin transliteration, the name may be written as ZHAN ZHENG XI, treating each character as a separate word. The name may also be transliterated as ZHAN ZHENGXI, treating the family name as one word and the whole given name as another word, similar to English format. In English name order, 展正喜 may be written as ZHENGXI ZHAN, because ZHENGXI is the given name, and ZHAN is the family name. However, ZHENGXI ZHAN may be too obnoxious, because no one writes the name in all capital letters. So, Zhengxi Zhan would be preferred. If the guy chooses an English name, such as Brian, he would be known as Brian Zhan.
In the first picture, the name is written as Zhan Zhengxi, because that is currently the set Western preference for writing Chinese names. In the second picture, note the exclamation points. That should tell you that the character utters each syllable separately and emphatically. That's why it is separated. In the third picture, Zhan Xixi may be a "little name"（小名）or a nickname（外号）. The "little name" is a special kind of nickname given at birth, making it different from a regular nickname.