Was there some kind of prejudice on companies against married women?
Not in the sense of sexism, but one important part of Japanese corporate culture is that one is intended to think "keiretsu" (company) before family or personal life.
As explained by many locals or foreigners, Japanese culture values long hours, hard work, and full dedication to the company.
It seems obvious that any married woman might have less time for the company if she has house, husband and children to take care of.
In universe, as Holly is devoted to her career, she wants to show the Japanese (no wonder that they did a background check on her!) that her (futur) divorce (thus, her maiden name back) kind of "frees" her from family obligation. She's a free woman with kids, and can work for the company as much as needed.