No.
The country does not have any regulations that require the use of three words, or prohibit the use of two-word documents. It only stipulates that uncommon words and alphabetic symbols cannot be used, but there is no stipulation on the number of words.
However, the Public Security Bureau and the Civil Affairs System recommend that residents give their children three-character names to avoid the excessive duplication rate of two-character names. From an expert's perspective, the more words in a name, the lower the repetition rate. Therefore, parents are encouraged to use fewer single words and try to name their children with two words.
Extended information:
Most Chinese names only have 3 characters. The more people there are, the more duplicate names there are. This is undeniable. We had the same name when we had a population of 400 million. In the Tang Dynasty, the population was less than 100 million. If you look through the dictionary of people's names, you will find that there are quite a few famous people with the same name. Therefore, in addition to correcting names, the ancients also had characters, numbers, and room names for the places where they worked, rested, and wrote. Duplicate names in modern times are even more inevitable, and it is difficult for the person who gave the name to avoid it no matter how hard he or she tries.
If you want to avoid duplication of names, you don’t need to resort to uncommon characters. In the past, we did not limit the use of characters in names. Rare characters are open to naming, and the rate of duplicate names is also very high! Of course, the fewer duplicate names the better, but duplicate names have not hindered our social life too much for so many years. The reason is: name is not the only parameter of a person, gender, place of origin, age, occupation, parents, and place of residence are all Those with the same name can be excluded. Addressing someone face to face is not a big deal since there are restrictions on the scope of activities.
Reference material: People’s Daily Online - Do not use uncommon words when naming