Using a former surname at work after marriage is not unique to Japan. In Japan, however, it often appears alongside the rule that two Japanese nationals who marry must choose one surname for both spouses to use legally.
Suppose a woman has worked for many years as Ms. Tanaka. When she marries, she and her husband choose Sato as their legal surname, so her legal surname becomes Sato.
Her clients, colleagues, business cards, email address, published work, and professional achievements may all be connected to the name Tanaka. If she also changes her name at work, people who have known her for years may not immediately realize that Ms. Tanaka and Ms. Sato are the same person.
She may therefore continue using Tanaka in meetings, emails, and other professional settings. The main reason is usually not to hide her marriage. It is to preserve the professional identity, relationships, and reputation she built under her former surname.
This does not mean that she has two legal surnames. Sato is her legal surname, while Tanaka is the name she continues to use at work. Her colleagues and clients may still know her as Ms. Tanaka, while her employer links that name to Sato for personnel records, identity checks, and other formal procedures.
Former surnames can now be used or shown alongside current surnames in more situations than before, although the exact rules vary by employer and procedure. This can make the use of a former surname more convenient, but it is not the same as both spouses legally keeping their original surnames after marriage.
In simple terms, her legal surname changed because the couple chose Sato as the surname they would share under Japanese law. She continues using Tanaka at work because that is the name under which she built her career.