According to Celeb Answers, there is a Japanese law that states if one of the parents of a child born in Japan is foreign, then the child must take the name of their Japanese parent. This explains why Naomi Osaka uses her mother's last name. Another reason why the tennis star may have elected to keep her mother's surname is that the United States did not help Osaka when it came to perfecting her tennis skills. 

When she applied to the Tennis Association of the United States to help secure funding for her training, Osaka was rejected because she isn't officially from the United States. This upset Osaka's father and pushed him to encourage the rising star to represent Japan instead of the U.S.

The final reason why Osaka may have decided to keep her mother's last name is that the marriage between her parents faced a lot of criticism. Osaka's mother came from a very traditional family who didn't approve of their daughter marrying outside of their Japanese heritage. This led to her being exiled from the family and could explain why she chose to give her daughters her last name. Regardless of which specific reason led to Osaka using the last name, her full name will go down in sports history.