Women frequently hyphenate their last names like Sarah Huckabee-Sanders. How would a Japanese woman with a Japanese maiden and married name added, hyphenate her last name?
Legally she cannot do this. Under Japanese law you can only have one surname registered on your residence and family register documents. If her husband is Japanese, then she will have to change her family name to his (as he is head of the household). If her husband is a foreigner, she is permitted to keep her family name (and is legally head of the household).
What she is known by informally is up to her but it's not her legal name in Japan. Japanese culture does not have a tradition of hypenating family names (or middle names). These are only permitted for writing foreign names in Japanese.
There is a convention for writing hypenated foreign names in Katakana but there is not one for hypenating native Japanese names in Kanji (as this never done).
Note that Japanese people have their family names first before their given names (so calling it a last name is discouraged to avoid confusion).