A definition the of the Sinosphere, or East-Asian Cultural Sphere, for those not into the whole brevity thing.
Breaking down the surnames in this regions:
a recent survey found that the list of Chinese surnames is a little over 4,000 (source in Chinese, Wikipedia article here ), in a country of 1.4 billion people.
Taiwan has about 1,500, many of those shared with China.
Korea, has around 286 total surnames in use.
In Vietnam, staggeringly, 14 surnames account for 90% of the population of nearly 100 million, with almost 2/5ths of the population having the surname Nguyen.
In stark contrast to this homogeneity, the current edition of the Expanded Dictionary of Japanese Family Names has more than 290,000 entries, and while many of these are historical and not in use, estimates place the average of Japanese surnames in use today around 100,000. Further, Japanese surnames tend to be polysyllabic, as opposed to the strictly monosyllabic surnames of the other cultures listed above.
So: given the high to extreme lack of diversity in surnames throughout the Sinosphere, were there historical or cultural factors that made Japan the exception to this rule? Conversely, were there shared historical factors on the continent that led to commonality and brevity of surnames that Japan did not experience? Or is this all a linguistic oddity? To that last point: it is worth noting that while most Chinese languages and Vietnamese are tonal, Korean is not, so this alone should not account for the discrepancy in Japanese.
The history of Japanese surnames is pretty distinct. Everyone having an official surname, registered with the government, is a relatively recent innovation for Japan, going back to the Meiji era decree in 1875 that every person needed to adapt a surname. Before that decree, through the Edo Period (1600-1867) it was generally only samurai (and the nobility) who were officially "allowed" surnames. In practice, a lot of the common population had surnames even before the Edo Period began, and continued to use them, they just weren't acknowledged by the government.
The largest category of Japanese surnames are geographic descriptors, telling where the family lived. for example "Yamamoto" = "base of the mountain", "Tanaka" = "middle of the rice paddies" etc. Not surprisingly, these sorts of descriptive names are very diverse.
In 1875, people had to come up with surnames for government purposes. Some people made official their long-standing surnames. Others used geographic descriptors for the first time. Herbert Plutschow in his book on the history of Japanese names: Japan's name culture : the significance of names in a religious, political and social context , writes that some Meiji peasants adopted the name of the landlord with "shita" (under) added to the end Shopkeepers and other merchants took on their business's names. Most interesting to my mind, Plutschow adds that monks, who'd just had the requirement for celibacy abolished and thus were founding their own families, often used religious names. The result was a huge variation in names.
I'm only basically familiar with Korea and China, so I can't contrast the development of names in those countries.