I think it varies with culture, but from my understanding, usually they take the first name of the two hyphens for their own marriage.

So you have John Doe and Jane Smith. They hyphenate their names as Doe-Smith and the children do as well.

Say they have a daughter Sally Doe-Smith who meets Tim Johnson-Star. So they marry and hyphenate their names as Johnson-Doe.

Yes, in examples like this, it still ends up as getting rid of the maternal aspect of it in the end…but the point is still that both parties are keeping part of and changing another part of their names. It’s not an all or nothing total switch of identity. The lineage is male, but the here and now is an equal compromise of identity.