Liuyi is a good choice as a nickname because it contains the time of the child's birth and is related to Children's Day. This festival means happiness, joy and beauty, which also adds a positive meaning to the child's name. In addition, the number "six" in Chinese characters has the meaning of auspiciousness and success, and can bring good luck to children.
So, if your child is born on June 1 and you like this holiday, then using "June 1" as a nickname is a good idea.