In stark contrast to the other answers I'm looking at here, I'm going to go on and say that... no... you're not wrong... it's not a "translation difficulty" ... it's not a homophone issue. The fact of the matter is there are a relatively small number of last names used by a huge number of Chinese people, even today. They are known, variously, as the 百家姓 - the Hundred Family Names - , or 老百姓 - the Hundred Old Names - or also quite tellingly as the 张三李四... literally the "Three Zhangs and Four Lis"... both of the last two are often used as colloquialisms meaning simply "everyone" or "the commoners." As you can see, even the Chinese themselves acknowledge and to an extent make light of the propensity for a huge proportion of the population to share identical surnames.

This is exponentially compounded by the fact that when you get into ancient Chinese histories, they are fundamentally and near-totally concerned with the major political actors. The Romance of the Three Kingdoms (and the historical Annals of the Three Kingdoms) is simply par-for-the-course in that they only care about the ruling families and pay not a whit of attention to the "smallfolk." Think of it, if you like (because I do) much like Game of Thrones... we all know the Lannisters, the Starks, and the Targaryens... but we rarely (if ever) hear about John the Blacksmith, or Edd the Potter, or Susan the Milkmaid. They're quite literally beneath the notice of the classical historians who were paid by the ruling dynasty to write very flatteringly about them, and very unflatteringly about their predecessor dynasty... they just didn't matter to them. Sadly what that means to people studying ancient Chinese history (and most ancient history, for that matter) is that you have a huge void of information on the vast majority of the populace. As far as the ancient historians were concerned, unless they were rising up in agrarian rebellion, they were simply a part of the landscape, and about as worthy of page-space as the resident goat population.

So that's a major factor. The ruling clans dominate the historical narrative, both politically and in terms of the people chosen to be written about. But that also doesn't solve the whole question of "why?" But there are a few other major factors...

Prior to the Warring States Period (ca. 5th c. BCE) only aristocratic nobility and royalty held surnames of any kind. Following the unification of the Qin Empire in the 3rd c. BCE, however, those noble names were more and more adopted by the lower classes as well (a similar thing would happen in Japan and Korea... though much later... which is a big reason for the Korean joke: you can't throw a coin off a building in Korea without hitting a Kim)

Imperial decree could and was frequently employed to reward loyal servants of the throne with the imperial surname of the age - the surname Kuang (鄺) is a good example of that - meaning: the State of Kuang in central China ca Han Dynasty (ca. 2nd c. BCE-2rd c. CE)

Likewise, occupation and official titles were adopted as surnames for entire lines. Examples include: official positions, such as Shǐ (史, "historian"), Jí (籍, "royal librarian"), and Sīmǎ (司馬, "minister of horses")... to noble titles like Wáng (王, "king/prince"), Hóu (侯, "marquis"), and Gōngsūn (公孫, "Duke's descendant")... down to the base levels of the social hierarchy, such as ... Táo (陶, "potter"), Tú (屠, "butcher"), Bú (卜, "diviner"), Jiàng (匠, "craftsman"), Wū (巫, "shaman") and Chú (廚, "cook").

Eventually as more and more people began to share the same surnames, it actually because enough of an issue that a subsequent line of surnames had to develop simply to differentiate one "line" of a family from another. (Back to my GoT reference: think of the Starks vs. the Karstarks)... As such markers of place within the birth order have also become used as family names. Meng (孟), Zhong (仲), Shu (叔) and Ji (季) were used to denote the first, second, third and fourth (or last) of a family's sons.

Another huge piece of the puzzle is ethnic groups - throughout its history, China has rubbed up against, made war with, and exchanged (voluntarily or otherwise) populations with non-Han peoples. These peoples were often given (or took) Sinicized names either based on or simply directly lifted from whatever the Chinese called them as a race. Examples include: Hú (胡, simply "barbarian/non-Han"), Jīn (金, "Jurchen"), Mǎn (滿, "Manchu"), Dí (狄), Huí (回) and Mùróng (慕容, of the proto-Mongol Xianbei people).

Then of course we get into the fact that there were family name changes happening frequently. As I mentioned, family names (and even the reigning imperial family name such as Liu (劉) during the Han Dynasty, Li (李) during the Tang, and Zhao (趙) from the Song could be given for exceptional service to the throne.

Other names came about to try to avoid the imperial names (imperial custom dictated that the sitting emperor's given name was legally taboo to write or use. As such individuals, families, and even entire places were occasionally changed to "avoid" the taboo). Maybe the most notable example was the switch from Shi (師) to Shuai (帥) to avoid conflict with the name of Sima Shi after his family seized control of Cao Wei and began the shortlived Jin Dynasty in the mid-3rd century. (You'll note in the character that they juts removed a single line from the top... that was enough of a change to pass).

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Enough yet? No? Okay, then here's the top ten list for Mainland China family names, with meaning/origins (all #'s/%'s from 2007)...

1.王 (Wang/Wong) - "King/prince" - obviously stems from the royal title - # of people ca. 2007: 92,881,000 (7.25%)

2.李 (Li/Lee) - "Plum" - traces back to Laozi, the founder of Taoism, used as the Imperial Clan name during the Tang Dynasty - #:92,074,000 (7.19%)

3.张 (Zhang/Cheung) - "Archer/bow" - occupation - #: 87,502,000 (6.83%)

So right there you've got more than 20% of the whole population with just 3 names. The rest were not given specific #'s or %'s, but were noted as each having more than 20,000,000 holders each!

4.刘 (Liu/Lau) - the clan name of Emperor Yao, one of the semi-mythical founding demigods in Chinese creation mythology, the Imperial Clan name of the Han Dynasty

5.陈 (Chen/Chan) - the State of Chen - place of origin

6.杨 (Yang) - "Aspen tree" - founded as a family name by the son of the Duke of Jin during the Spring and Autumn Period, surname of royal family of the Zhou Dynasty (8th-5th c. BCE)

7.黃 (Huang/Wong) - "yellow" - stems from the Yellow Emperor, the traditional founder of the Chinese people (Along with Emperor Yao, above)

8.赵 (Zhao/Chao) - the State of Zhao (Zhou Dynasty) - place of origin

9.吴 (Wu/Ng/O/Ngo/Woo) - the State of Wu - place of origin

10.周 (Zhou/Chow/Joo) - the Zhou Dynasty

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Hope that helps! If you're more interested in Chinese history may I invite you over to The History of China Podcast. We're in the middle of the Tang Dynasty right now (round about the year 730 CE). Cheers!

Some of that is weirdness from transliteration. There are at least six surnames that are transliterated simply as Li, for instance. Other surnames are less extreme examples: Yu and Ji come to mind. Sometimes the different forms are respected (Lü vs Lu), sometimes they're not.

The language barrier certainly explains the apparent scarcity of Chinese surnames. Adjust for that and Chinese surnames essentially follow the same distribution curve as other cultures.

There's an expression in Chinese, the "old one hundred surnames" (老百姓, lǎo bái xìng), which refers to the common people or general populace. While this expression is very old, appearing for example in the Analects, it is probably more reinforced by a Song dynasty poem called The Hundred Surnames which was traditionally used as a teaching aid for students in China and is literally just a list of some four hundred of the most common surnames.

In short, the recognition of the fact that there aren't very many Chinese surnames is not new. Even today, China has many fewer surnames than other large nations. In part this is because of how surnames work in different cultures and languages. In English, for example, many surnames are derived from professions (Smith, Carpenter, Baker, Wright, etc.), patronymics (Johnson, Jackson, Thompson, etc.), or even personal features (e.g. Bronson) or places of residence (Barlow, Blaisdell, etc.). What all this is meant to show is that it has been historically relatively easy to generate new surnames in English, but these linguistic processes are not really present in Chinese, and as a result, the number of surnames has not grown or even changed too much over time.

But just to be thorough, let's see if /u/keyilan can be summoned for a more detailed answer.

It's also worth noting that, depending on where you're from, you may have inflated assumptions about the diversity of last names. In cultures where all names come from the same source language, it's not that unusual even today for a small handful to account for nearly all the population; in extreme cases (like Kim in Korea and Nguyen in Vietnam) a single name can account for more than a quarter of the people. So if you live in a multicultural society, you might not realize how common this actually is.