I don't know how much this really counts as analysis, but I noticed that the topic of names repeats itself a lot in No. 6. There are three type of characters as far as I'm concerned:
1.
Characters with names: that's a pretty common thing that I have nothing to say about. Notice that the only characters that have actual names are either from No. 6 or originally from around No. 6 (such as Rikiga). Also, Shion's name being a flower is mentioned quite a lot. I wondered for a while about Yoming's name, because (I might have already said it somewhere) it sounds more Chinese than Japanese to me (than again I don't speak Japanese and I barely speak Chinese so...) If anyone knows how Yoming's name was spelled in Japanese or in Chinese that could shed some light on the subject.
2.
Characters with no names: there are several characters that are only referred too by their title, such as the man in the lab coat, Nezumi's grandma, Shion's father, Inukashi's mother.... I tend to think that these characters don't have names only because they only took part in the story in other people's thoughts, or in the man in the lab coat's case, because Safu simply didn't know and couldn't ask for his name. Shion's father can also be related to the next category, because he called himself 'Shion' in beyond.
3.
Characters that go by nicknames: yes, that's right. Nezumi's turn. Of course, he isn't the only one. I have to admit that I have very little to say about Nezumi's name, mostly because I think he doesn't care about this sort of things. Also, Eve? Such as, the person who ruined paradise by gaining knowledge? I wonder why that sounds famili--oh wait the beginning of No. 6. More in the 'I don't have a name 'cause I don't give a ****' category, Inukashi. Nothing more to add about that. But then we have other characters with pretty interesting concepts.
-Fennec: of all animals Atuko Asano could choose, fennec? And for a pretty important and cruel person, he's taking this sort of offensive nickname kinda easily, don't you think?
-Rou: as I said before only people from No. 6 have actual names. Did he change it in order to get rid of his past? Also, was he really an Elder when he arrived to that place?
-Elyurias: my personal favorite, Elyurias doesn't have a name and in reality, is by itself a being that can't be defined. Pretty cool, in my opinion
-No.6: I realize this is not a character *but* why name your cities after numbers? Don't you have more creative things than that? Also, they chose to keep the name after they started rebuilding it, which is pretty strange.
After writing this I realized that Sasori does have a name and he's not from No. 6 but nah you get my point. (Sasori is my favorite underrated character tbh)