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Note: This is not every time they insult/make fun of each other. For example Dazai tends to say things like he'll put a curse on Chuuya to remain short whilst he grows tall, more than name calling. However this list is only name calling.
Dazai about Chuuya:
Kid
Pip-squeak (Uses more than once)
Little fairy
A child
Schoolboy (Uses more than once)
Little man
Filthy dog
Chuuya - He calls Chuuya by his name for the first time in the arcade, Chuuya then tells him not to use his name. After this Dazai repeatedly says his name over using nicknames.
Chuuya about Dazai:
Kid
Surprisingly gutsy kid
Little shit
Little punk
Dumbass
Lil twig
Mummy boy (Uses more than once)
Little wimp
Bandages
Idiot
Twisted freak
Little suicide-obsessed- (he's cut off before he finishes this one)
Sly dirtbag
Slimeball (Uses more than once)
Crafty son of a bitch
Sly bastard
Demon
Weasel
Dazai - He calls Dazai by his name for the first time during their fight with Rimbaud when they agree to work together to defeat him. However, he still mixes in name calling along with using Dazai's name.
BONUS - Names Chuuya uses for other people:
Old man - Hirotsu
Old fart - Hirotsu and the Old Boss
Doc - Mori
Bastard - Mori
Piece of shit - Mori
Damn octopus - Mori
Gramps - Random GSS member
Dumbass - Shirase
Ma'am (Ane-san) - Kouyou. (She also calls Chuuya 'Young man' just before this. They both disapprove of being called these.)
Boss - Mori
Randou - Rimbaud (as far as I could see Chuuya mostly used his name, though I may have missed a nickname)
A thing I noticed with Dazai is that he generally calls people by their names. He calls Hirotsu, Mori and Kouyou all by name. With Mori it sometimes feels like that's the insult, he knows he can get away with disrespecting him this way, so he doesn't call Mori his Boss. Similarly he only starts calling Chuuya by name after he's told not to. He also prefers coming up with imaginative insults/scenarios rather than name calling, though he's not above it, so his list is a lot shorter than Chuuya's.
Chuuya however, uses nicknames for practically everyone, they just get more polite the more he respects them. Mori goes from 'Bastard' and 'Octopus' to 'Boss', once he gains Chuuya's respect. Rimbaud felt like the exception because Chuuya kept calling him Randou during their fight.
I also think it's interesting that Chuuya calls most adults something to do with being old/older. I don't know whether it was intentional or not, but to me, this emphasizes how Chuuya is used to being solely around other children. Even Kouyou who is only nineteen, is labeled as older to Chuuya, probably because there were no Sheep her age. In both the anime and the manga they are all depicted as younger teens around the same age as Chuuya.
Ane-san is also a mafia title, so it could just be that, but I do think Chuuya is genuinely not used to being around adults and that not meaning danger.