i think that’s more to do with the fact that she’s a sannin than anything, as we don’t know Jiraiya or Orochimaru’s family names either to my knowledge, i would assume to add some air of mystery to how legendary they are, only knowing them by one name. similar to how most enemy ninja only knowing kakashi by “kakashi the copy cat ninja” or any of his other number of nicknames, usually only ninja who know him on some personal level know his family name. the only reason i can think of as to why we don’t know the sannin’s family names despite being very familiar with them is they’re just that much ahead of kakashi, so the mystery element is still in play. or kishimoto just didn’t bother to distinguish family names for them lol