What do you call a daughter with the same name as her mother? Is there a female equivalent for 'junior' in the english language?
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 same name.
For fathers and sons who share a name, you sometimes see the French words "père" ("father") and "fils" ("son") used instead of "senior" and "junior". In the same way, one could perhaps use "mère" and "fille" for a mother and daughter.
However, it should be noted that I can find no actual evidence for this usage. And anyway, even "père" and "fils", though well-established, may strike some English-speakers as pretentious.