Not sure what the legalities are/were in Sweden, but in the UK there's no "should be" as a woman's surname does not have to legally change upon getting married. If they choose to, they can change it on passport, driving licence etc, which then becomes a legal change, but if they choose not to do that then their surname is still legally whatever their pre-marriage one is. This is the same for same-sex married couples as well.
It was uncommon for many years for famous people to change their "stage" names upon getting married. The Spice Girls, despite bleating on about "girl power", seemed to make it fashionable for famous women to adopt their husband's surnames. Cheryl Tweedy might have been better off sticking with that name as she's been married so many times now that her surname changes more often than Madonna's hair colour used to. I think she now just goes under the name "Cheryl".
Not sure if Agnetha's and Frida's names were "Agnetha Fältskog-Ulvaeus" and "Anni-Frid Lyngstad-Andersson" respectively. I do remember seeing their names occasionally given as these during their married ABBA years.