How common are single-syllable Chinese given names — names that take just one Chinese character to write?
Much less common than they were in the 1980s and 1990s. The downward trend is not likely to change, because China wants to avoid being a place filled with the equivalent of John no-middle-name Smiths.
The proportion of two-character names (i.e., a single-syllable family name plus a single-syllable given name) in China increased from 7.6% in the 1960s to peak at 27.6% in the 1990s. But the figure has now fallen to just 6.3%.
Although some of the three-character names will be those of people with two-character family names and single-syllable given names (as opposed to single-syllable family names and two-syllable given names), the figure is statistically insignificant, as only 0.11% of people in China have two-character family names and only about 6.3% of them will have single-syllable given names (or only about one person in fifteen thousand).
Although in the chart below the number of people with names totaling four or more characters/syllables is small (and largely within minority groups), such names have been on the increase, growing from from just 0.3% and 0.4%, respectively, in the 1950s to 1.6% and 1.7%, respectively, at present.
In Taiwan, single-syllable given names are much less common than in China. Also, in Taiwan the majority of those with single-syllable given names are female; I don’t know if that tendency exists in China as well, but I suspect that it does.
Source: 《2020 nián quánguó xìngmíng bàogào》 fābù (《二〇二〇年全国姓名报告》发布), Gōng’ānbù wǎngzhàn (公安部网站), February 2, 2021
Further reading: 85 percent of Han in China have two-syllable given names: report, Pinyin News, August 10, 2008
Thanks to Qin-Hong Anderson for her input.