Odeda is correct. No way Bat Zion is a parent or Surname. It’s a derivative of Ben-Zion (son of Zion), a reasonably common male name.
Bat-Zion (daughter of Zion) would have been pretty much an unheard-of name in the era in which she was named. More likely she adopted that Hebraicized name at some point.
my mother was named Tryna but adopted the minimally similar Hebrew name Tamar in her teens. All in New York City, not Israel. And her tombstone now says Tryna-Tamar.
