Why was dynasty synonymous with nation in Korea but not China?

How come China gravitated towards being referred to as Zhongguo over dynasty names, while the Korean dynasty name of Joseon (and later Great Han) survive to this day as names for the Korean nation? Furthermore, is there a way that Chinese nation-state could be referred to by a dynasty name instead of as Zhongguo? Also, what accounts for Korea not having a name for the Korean nation independent of dynasty name, like the Vietnamese or Japanese (or indeed, China)?
 
You're getting confused because the distinction you make between "dynastic names" and "country names" don't exist. Names like Han, Chosŏn, or Qing aren't the names of the dynasty (which would be Liu, Yi, and Aisin Gioro respectively), they're the names of the actual state. This is how they are always referred to in East Asia; as guo hao, the "name of the state."

Consider the very first Chinese empire, the Qin. The Qin weren't called that because that was the name of their dynasty, it was because the empire was founded by the Kingdom of Qin conquering all other Chinese kingdoms. Qin was always the name of the state.

Same with Han, with Tang, with Song. They all refer to regions in China where the founding emperor built up a base.

With Ming and Qing it's a bit different, because these state names are ideological. But these are still not dynastic names, any more than Burkina Faso is the name of the Burkina Fasoan government as opposed to the actual country.

Because in East Asia, a state was associated with a ruling dynasty to a level greater than in Europe, the name of the state changed when the ruling dynasty was deposed. But "Ming" or "Chosŏn" were never dynastic names, even to the extent that Osmanli was in the Ottoman empire. Imagine: in the sixteenth-century Ottoman empire, no Armenian merchant or Egyptian peasant would think of himself as an Osmanli, only as a subject of the Osmanli class (which referred solely to the bureaucrats and officers who served the House of Osman). In the sixteenth-century Ming empire, every Chinese person would think of himself as a "Ming person."

Because the state name "Qing" wasn't exactly popular following the Xinhai Revolution, the revolutionaries used Zhonghua as the name of their state, an antique word referring to Chinese civilization. For a European analogy, imagine that the name "France" was so closely associated with the Ancien Regime that Robespierre changed it to "Gallia."

Because the Yi weren't nearly as unpopular as the Aisin Gioros, and because there was no similar antique word referring to Korea that was palatable to Korean nationalism (most ancient words for Korea are from a Sinocentric perspective), Koreans stuck with Chosŏn and Taehan.
 
The name of the chinese people (which one could call the chinese nation, arguably) is Han, which directly comes from the Han dynasty.
Anyway, Zhongguo means "Land of the Middle", which IIRC is tied to their dominant power in Asia: they were the litteral center of Asia, through their unmatched power. They could end up not being called that way if they have a early, long-term rival, though I'm not quite sure how that would happen... But if it does, then they would have to call themselves Hanguo, I suppose.
 
You're getting confused because the distinction you make between "dynastic names" and "country names" don't exist. Names like Han, Chosŏn, or Qing aren't the names of the dynasty (which would be Liu, Yi, and Aisin Gioro respectively), they're the names of the actual state. This is how they are always referred to in East Asia; as guo hao, the "name of the state."

Consider the very first Chinese empire, the Qin. The Qin weren't called that because that was the name of their dynasty, it was because the empire was founded by the Kingdom of Qin conquering all other Chinese kingdoms. Qin was always the name of the state.

Same with Han, with Tang, with Song. They all refer to regions in China where the founding emperor built up a base.

With Ming and Qing it's a bit different, because these state names are ideological. But these are still not dynastic names, any more than Burkina Faso is the name of the Burkina Fasoan government as opposed to the actual country.

Because in East Asia, a state was associated with a ruling dynasty to a level greater than in Europe, the name of the state changed when the ruling dynasty was deposed. But "Ming" or "Chosŏn" were never dynastic names, even to the extent that Osmanli was in the Ottoman empire. Imagine: in the sixteenth-century Ottoman empire, no Armenian merchant or Egyptian peasant would think of himself as an Osmanli, only as a subject of the Osmanli class (which referred solely to the bureaucrats and officers who served the House of Osman). In the sixteenth-century Ming empire, every Chinese person would think of himself as a "Ming person."

Because the state name "Qing" wasn't exactly popular following the Xinhai Revolution, the revolutionaries used Zhonghua as the name of their state, an antique word referring to Chinese civilization. For a European analogy, imagine that the name "France" was so closely associated with the Ancien Regime that Robespierre changed it to "Gallia."

Because the Yi weren't nearly as unpopular as the Aisin Gioros, and because there was no similar antique word referring to Korea that was palatable to Korean nationalism (most ancient words for Korea are from a Sinocentric perspective), Koreans stuck with Chosŏn and Taehan.
I'm aware that dynasty names aren't the names of the ruling families themselves, but the fact is that when a new dynasty was formed they renamed the country. That is what I'm talking about (which is why I said dynasty name, not dynastic name).

Also, from a bit of cursory research, it seems like the shift towards "Zhongguo" happened during the Qing dynasty, so it seems less like a throwback to the romantic past and more of a gradual evolution. More information on this would of course be appreciated.
 
Also, from a bit of cursory research, it seems like the shift towards "Zhongguo" happened during the Qing dynasty
During the High Qing, zhongguo was largely synonymous with neidi and referred solely to the Eighteen Inner Provinces that were traditionally Han-majority. The greater use of zhongguo in the nineteenth century is because of Western intrusion, which demanded a better translation of the Western concept of "China" than "Great Qing Empire."
 
During the High Qing, zhongguo was largely synonymous with neidi and referred solely to the Eighteen Inner Provinces that were traditionally Han-majority. The greater use of zhongguo in the nineteenth century is because of Western intrusion, which demanded a better translation of the Western concept of "China" than "Great Qing Empire."
So had the Qing been butterflied, would it mean that Zhongguo wouldn't be used as much? I'm wondering whether or not a republican China could maintain a name like Song or Ming.
 
So had the Qing been butterflied, would it mean that Zhongguo wouldn't be used as much? I'm wondering whether or not a republican China could maintain a name like Song or Ming.
I doubt it. When referring the civilization as a whole or the area geographically,the terms Huaxia and Zhonggua were often used.The term Zhonggua was often thrown around to signify legitimacy as the Middle State.
 
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