Indeed, in the comics the females have a first name and add their father's name to it, as in Kara Zor-El (Kara, daughter of Zor-El).
But I cannot remember any place where the name of a married woman is mentioned, it might actually change like a woman's maiden name (to the husband's full name or family name, it would make sense in a patriarchal society), it might get deleted after marriage (which would explain why Lara is only ever known as Lara) or stay and probably get the family or full name of the husband added.
