We have only confirmation of Sadie's surname, and it is quite common for parents and children to have different surnames. It is not confirmed that Barbara's surname is Miller as well.
Barbara, for example, could have kept her maiden name, but given Sadie the surname of her father (or other mother) (if Sadie does/did have another parent). Barbara could have a double-barreled surname from marriage, such as Jones-Miller, while giving simply her partner's name, Miller, to Sadie.
Ah I see, thats kind of like my parents. Good thinking on your part, although i'm not sure if its common I never met anyone besides my parents who has done that. Maybe you could ask the crewinverse on their twitter and see if we can get some confirmation on this.