Traditional Chinese characters can be used, but only in daily life. The name cannot be in traditional Chinese.
When it comes to work, schooling, medical treatment, household registration, and document processing, you must write in simplified Chinese characters, because our mainland adopts simplified Chinese characters.
The simplification of Chinese characters began in 1956, and by March 1964, the "General List of Simplified Characters" (hereinafter referred to as the "General List") was formulated. In 1977, the "Second Chinese Character Simplification Plan" was launched, but it was opposed by many people.
In June 1986, the State Council approved the State Language Commission's "Request for Instructions on Abolition of the Second Chinese Character Simplification Plan (Draft)" and on Correcting the Confusion of Chinese Characters in Society. From then on, the "Two Simplified Chinese Characters" was discontinued.
Extended information:
The "List of Standard Words for Personal Names" stipulates that there are restrictions on the words used in naming. The names used for newborns in my country will be selected from 8,000 standardized words.
51 variant characters that were once abolished but are still widely used and banned are "released" and restored to use. The restoration of variant characters respects social habits and facilitates people's word use needs. The character list includes 51 variant characters in the "First Batch of Variant Characters Collection List", which are mainly used as names of people and places.
For example, "円" was originally regarded as a variant of "Zhe". After investigation, it was found that more than 20,000 people across the country had this character in their names. Experts believe that the two "吉" characters in the character "喆" look very peaceful when placed side by side, and are more suitable for naming than the character "Zhe", so they included it in the third-level character list, specifically for use in names.
The new word list provides a lot of convenience for the public to choose names. For example, in order to take care of the common use of the characters "nupang" and "caotou" when naming girls, the word list specially includes some uncommon "nupang" characters.
Reference material: Baidu Encyclopedia - General Standard Chinese Character Table