INTRODUCTION TO THE CHINESE NAME
The American-Based StackExchange Network ranks below Quora in Alexa. Quora receives a lot of traffic, including traffic from native Chinese speakers with professional competency in at least written English and fluently bilingual heritage speakers. StackExchange, on the other hand, is kind of a niche website, so the population base will definitely reflect this, as of now (January 15, 2019). Therefore, I am going to assume that any person who is reading this will not be familiar with the Chinese language, let alone Chinese culture and society.
The Chinese name is a complex topic by itself. The Wikipedia article gives a primer to the Chinese name, and like American names, there are naming trends, regional preferences, and a spectrum of names ranging from very masculine to very feminine. The Chinese people of the People's Republic of China are made up of the Han people and 55 ethnic minorities. The ethnic minorities may or may not have a typical 中华民族 (pinyin: Zhong Hua Min Zu) name pattern.
Chinese Name: 趙貴翁 (Traditional) / 赵贵翁 (Simplified)
The 赵 surname is one of the most common surnames among Chinese people. As a surname, it is meaningless. Because the surname is supposed to be meaningless, taking account of the logogram's meaning is a part of making the pun. My monolingual Chinese dictionary (新华字典) says: 战国国名, which means the Warring States. (Sorry, but my knowledge of Chinese history is lacking, so I can't comment on the corrupt aristocracy at that time.)
贵 is part of the given name. aristocratic is one of the meanings of this character. 翁 is the other part of the given name. old man is one of the meanings of this character.
This name is a pun, if you look at the name at multiple levels. On one level, 赵贵翁 looks like a believable Chinese name. On another level, it looks like a descriptor for a character. 赵 may be taken as an adjective, referring to the Warring States time. 贵 may be taken as an adjective, referring to the high status. 翁 is a noun, referring to an old man. I must note that, in Chinese literature, both descriptors and personal names (姓名) can be used as character names. And I think some works in English literature are also this way. Sometimes, a character may be labelled "The Big Bad Wolf" or "The Old Man".
Chinese Name: 古久 (Traditional and Simplified)
古 is a surname. It is not a common one, but it is a documented surname. As a surname, it means nothing. As a logogram, it means "ancient". 久 can be selected as a person's given name. It means "a long time".
This name is a pun, if you look at the name at multiple levels. On one level, 古久 is a plausible personal name (姓名). On another level, 古久 refers to China's long ancient history. When 古时候 is used in Standard Written Chinese, it refers to "ancient times" -- 古 means "ancient" or may refer to "ancient times"; 时候 means "time". In a Chinese context, "ancient times" is anything up to the Republic of China era of Chinese history, because the Republic of China era is when China becomes modern. As previously mentioned, 久 means "a long time". On a grammatical level, 古 is symbolic of ancient times and may be taken as the topic in a topic-comment structure. 久 is the adjective. In the Chinese language, adjectives are also static verbs. So, 久 is the verb. The Chinese language is a SVO language. So, 古久 means "[ancient times] [stretches a long time]".
Also worth mentioning is that A Madman's Diary was published in 1918, as part of the New Culture Movement, which sought to criticize the old way of life and thinking and modernize China in order to keep up with the rest of the world. China was a great power, but then it got humiliated by foreigners/barbarians - Japanese people and Europeans. So, of course, some measures needed to be done in order to make China great again.
The work is to make fun of the old Classical Chinese literature and the associated Confucian values. A slightly off-topic but interesting note: my cousins grew up in China. One cousin sent his elementary school literature books to me for study of the Chinese language. The books are structured like these textbooks for Overseas Chinese children, but they are more tailored to Mainlanders, because (1) Mainland children can identify with specific Chinese holidays more, (2) Mainland children don't need to have English translations mainly because they can't read English, and (3) you don't have to describe the restaurant next door is a Chinese restaurant if you are already in China. But anyway, in one story I read, it is about 孙中山 (Sun Yat-sen). As a child, he went to school. The point of school was to recite literature. But Sun Yat-sen thought the literature was meaningless to him (duh, it's written in Classical Chinese) and asked the teacher for an explanation. The teacher replied that he was supposed to recite the literature, and he would later come to understand in the future. Then, one classmate asked him why he asked the teacher. Sun Yat-sen said, even if he was beaten, it was important to understand than to memorize blindly. As you can see in this story, Sun Yat-sen is challenging the old way of life and thinking, by becoming more of a critical thinker. This completely ties in with the New Culture Movement.