Progressive people are plagued with naming conundrums when getting married and having kids. Who takes who's name and does that imply something about the union?
If each person has <first name> <middle name> <last name>, each spouse can take on the last name of the other spouse as a replacement middle name or new second middle name.
A daughter's name will be
<first name> <father's last name> <mother's last name>
A son's name will be
<first name> <mother's last name> <father's last name>
The daughter and son naming conventions can be switched, but knowing the convention through generations makes it possible to trace family lineage either matrilineally or patrilineally.
As DNA is recombined with the conception of a child, so names are recombined.
