According to the FindMyPast blog, the original 1939 register was updated until 1996, so as to mention changes of name and deaths.
So if your mother had already married by 1939, she wouldn't have her maiden name mentioned. If she married in 1940, she will be listed under her maiden name, and some sort of marker (extra columns?) added to give her married name. If she died before 1996, that date too should be marked up in the register.
If an entry mentions a person's death, of course, that person's details ought not to be redacted, even if they were born well after 1915.