Chui or Tsui is an ancient Chinese family name relating to a clan in ancient China. The Chinese character is 徐 , as is used interchangeably in Hong Kong traditional Chinese, Cantonese with and in Taiwan Traditional Character using Yun biu -音標;
This sound differently from "Xu" 徐 in Mandarin Pin Yin.
This Chinese character literally means slow.
As distinct "Hui" in Cantonese or "Xu" 許 in Standard Mandarin Pin Yin.
There is also "Cui"崔 in Standard Mandarin Pin Yin also a family name.
References
Chui Wikipedia(Text) CC BY-SA