In my country, there is no distinction between Last name and Birth Surname, so it's not clear which one should be used, and often collaborators in my tree use them in an inconsistent way.
I have found that if I backup my tree using a GEDCOM export, I must choose between saving the Last name and the Birth Surname. However, no matter which option I choose, both exports will be missing some lastnames.
I don't know if there would be the possibility of exporting both of them in separate fields in the same .ged file.