They can, but it is less common, in part because it is less
common to name a daughter after her mother. One example of this
being done is that Warren Buffett's wife is named Susan and his
daughter is also Susan. The daughter is called Susan, Jr.,
throughout his biography. ---- Traditionally (but not always) women
would take the last name of their husbands when they married. So a
woman called Alice Lassiter, Jr. who married Ned Burns would become
Alice Lassiter Burns. So the "Jr." would go out the window in her
case, eventually. Therefore most parents reserved the "Jr." for
their sons, whose names don't change.