While you may choose a nickname to differentiate in daily use, for legal or genealogical purposes, she is a "junior." According to Wikipedia:
The most common name suffixes are senior and junior, most frequent in
American usage, which are written with a capital first letter ("Jr."
and "Sr.") with or without an interceding comma. The British English
abbreviations are "Jnr" and 'Snr', respectively. The term "junior" is
correctly used only if a child is given exactly the same name as his
or her parent...
Although there are instances of daughters who are named after their
mothers and thus use the suffix "Jr." (such as Winifred Sackville
Stoner, Jr., Anna Eleanor Roosevelt, Jr., and Carolina Herrera, Jr.)
or after their grandmothers with the suffix "II", this is not common.
Usually, the namesake is given a different middle name and so would
not need a suffix for differentiation. Furthermore, once the woman
marries she would most commonly take the surname of her husband and
thus do away with the generational suffix. The title "Jr." is
sometimes used in legal documents, particularly those pertaining to
wills and estates, to distinguish among female family members of the