I'm pretty sure Chuchu is a nickname (it means "cute"), although I guess with the propensity for Chinese people to name their girls with cutesy double-syllable names, one could imagine that it is her real name.

The author didn't bother giving her one. :( Afaik, her canon name is "mute girl" - which is at least in line with "Glasses" and "Sleeveless Jacket" as character names.

hopefully at some point everybody can have nice things?

This! Made me laugh! :D