I have heard of:
• Neither changing their last names.
• Both changing their last names to a portmanteau of their former names (i.e., 'Baker' and 'Johnson' to 'Jonker').
• Both changing their last names to the aforementioned hyphenations (i.e., 'Baker-Johnson' and 'Johnson-Baker').
• Both changing their last names to the last name of an historical LGBTQ person.
• Only one taking on their partner's last name.
It doesn't really matter, of course, as long as it is done legally. There are even legal procedures to change one's name without being married at all!
_________________
No love for Hamas, Hezbollah, Iranian Leadership, Islamic Jihad, other Islamic terrorist groups, OR their supporters and sympathizers.