That's definitely possible, especially since @anyudr also mentioned that they thought of the names as common. But with the context of the novel and just how the main character speaks, which both point to the setting being modern Beijing or somewhere similar, I'm hesitant to say that the disconnect is due to a difference in dialects/cultures. It does seem to be what the author is trying to get across though, so culture aside, I'll probably just translate as it is.
小红, is likely a nickname. It is use in many primary school math question like 小红有2个苹果吃了1个还剩几个? Bob have 2 apple at first, how many apples would he have after he ate 1? Its originalted from the book Dream of the Red Chamber where the character 红儿, real name 林红玉. But due to typo error or something it become 林红儿 later know by the nickname the community give her 小红. Due to the common usage, even people who have not read dreams of red chamber knows the name 小红 hence its widely use in writing where writer are too lazy to think of a name, and as a widely know name such as math questions. Its usage is similar to Bob, Bill, Joe, in your math papers
云汐 is the name, why do people think 彩鳯 is a name? 在那个起名小红,彩凤遍布的年代,云汐这名简直让我妈惊为天人,于是决定无论她肚子里是男是女,就叫云汐。 That crown with nameless sense, in the age of digital advancement, My mom was a genius to think of a name Yun Xi, she decided that be it a girl or a boy, his name will be Yun Xi. You might need to edit the sentence. I live in Central China, I don't know English. Basically 小红 is a placeholder for the babie in the womb. It's not a 小名, as it's a common for 小名to be desided after birth by the baby's God father. 改; God father 是干爹,不是godfather 神父
That crown with nameless sense, in this day and age, My mom was a genius to think of a name Yun Xi, she decided that be it a girl or a boy, his name will be Yun Xi. 外语太难了,你也差不多懂了吧。
Phoenix is an auspicious creature in China, which represents luck. Many Chinese (both low-class and middle-class I should say) will include“凤”in their children's name because they wish their children good luck, so “彩凤”became a really common name in China.
我的意思很简单, 我的解释是在一个小红和彩凤常用的年代。还有干爹是stepfather,foster father,adopted father,godfather是在神父认同之下的。 神父是priest