tonosaman is a play on tonosama 殿様 feudal lord from the edo period, and the 'man' ending in american style superheros, to get a modernised feudal lord character thats also a superhero
new edo city is a contradiction, because edo is the old name for tokyo.
in the edo period (tokugawa shogunate) edo was still called edo and it was the practical capital where the shogun ruled, but the emperer and the official capital was kyoto. it changed officially afterwards, with the name change. tokyo 東京 is eastern capital
so its the same thing, a modernised historical edo setting, implying that tokyo either never happened, or it went back to being the edo period and edo city later
the logo says 'great edo warrior: tonosaman'. the character on the fan and his forehead is 'tono' btw.
tonosamans suit looks sprt of futuristic as well, implying its not a completely historical setting. and tonosaman hei/3 has a metal arm.
tonosamanjuu that yahari sells in 1.4 is a play on tonosaman and manjuu (steamed bun)
akudaikan is 悪 (bad) and 代官, an official. in the edo period a local governor. collectes taxes and also in charge of legal things. got called a magistrate, which is like a judge in a minor court. wikipedia actually has a whole section called 悪代官, apparently its a thing in pop culture that the daikan is corrupt, and apparently people call bosses that give them hard work daikan
himesaman from 姫様 is just from prinesss. basically 'princessman', which doesnt make much sense in english, but the actual meaning of 'man' isnt relevent here, its just used to mean superhero.
tonosaman hei 丙 means third. it can be third as in tonosaman 1, himesaman and hes the 3rd, but apparently in the show he had 2 brothers who are 1 and 2. (thats what the screenshot says)
丙 comes from an alternate numbering system from historical china. 甲乙丙丁 etc. one of the current uses is in legal contexts numbering parties in a contract
his spear is also in the shape of that character
and torisaman in kurain is 鳥様. 'bird lord', 'bird princess,' or something
"warrior from the land of the dead, torisaman"
the person in kurain who was killing people for the government was torihimesama 鳥姫様, Bird Princess. so in the screenshot naruhodos connecting the way mayoi looks up to the person in kurain to the tv show
btw the sama 様 that they all have is just an honourific form of address. its one of the most polite/respectful ones
