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!
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The mere fact that science may not yet adequately explain an object, event, or experience does not mean the immediate explanation should automatically default to a conspiratorial, extraterrestrial, paranormal, or supernatural cause.