What does the Vietnamese name "Nguyen" actually mean?

Question

In 13th century Vietnam someone overthrew the Ly dynasty and forced all the members of that family and its nobles to change their name to Nguyen.

When that dynasty was overthrown, its supporters changed their name to hide from the next dynasty.

This happened several more times and as a result, nearly 40% of Vietnamese have the name Nguyen.

Internet says the name derives from a Chinese name "Ruan." Ruan was a place fairly north in China but its people were displaced and moved south. There is an instrument with the same name.

Why was Nguyen chosen to be the loss penalty for the defeated dynasty? If I go by the etymology the internet claims, perhaps the new king was trying to drive home the point that his quarry were really foreigners who drifted in. At one point, the founder of the Ly Dynasty's founder was from what is now Fujian, China, but not Ruan. It would seem that if he wanted to invoke the foreignness of the Ly, he should made the people change their name to Fujian.

Does anyone have a good answer to what the name means and why the King chose it?

Answer 1

To quote a relevant article on Atlas Obscura:

Ruan itself might come from an ancient Chinese state of the same name, or maybe from the ancient lute-like instrument also called a ruan. Who knows? Either way, it seems likely that some mid-level Chinese bureaucrat, in seeking to figure out who actually lived in his newly conquered Vietnamese territory, simply decided that everyone living there would also be named Ruan—which became Nguyen.

It is implied that Ruan may have been the family name of the bureaucrat who chose to give the subjected population the same name, although there is no direct evidence of this. In any case the point is that the name itself was basically arbitrary and probably didn't have any literal meaning of siginificance to the people who it was originally imposed on.

As for how the name became so popular over time, this same article emphasizes a key point related to this arbitrariness:

The last name, in Vietnam, is there, but just isn’t that important. And when it’s not that important, you might as well change it if a new last name might help you in some way. [...] Vietnamese people have tended to take on the last name of whoever was in power at the time. It was seen as a way to show loyalty, a notion which required the relatively frequent changing of names with the succession of rulers. After all, you wouldn’t want to be sporting the last name of the previous emperor.

To elaborate on the relevant history a bit, quoting now from Wikipedia:

In 1592, on the collapse of the Mạc Dynasty, their descendants changed their surname to Nguyễn. When the Nguyễn Dynasty (the descendants of the Nguyễn Lords) took power in 1802, some of the descendants of the Trịnh Lords fearing retribution changed their surname to Nguyễn, while others fled north into China. The Nguyễn Dynasty awarded many people the surname Nguyễn during their rule, and many criminals also changed their surname to Nguyễn to avoid prosecution. As with other common surnames, people having this surname are not necessarily related.