Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
There is nothing wrong with naming the daughter after her mother, if the mother’s name is a name that is permissible.
Answering your question, the Fatwa Center at Islam Q and A, states:
There is nothing wrong with naming the daughter after her mother, if the mother’s name is a name that is permissible, because the basic principle with regard to names is that they are permissible, and no names are disallowed unless they are prohibited according to the Islamic teachings, such as names that are indicative of servitude to anything other than Allah, or names that are reprehensible and off-putting.
The prominent Saudi scholar, Sulayman Al-Majid said:
“I do not know of anything in the Islamic teachings to disallow naming a daughter after her mother. Based on that, there is nothing wrong with doing that.”
With regard to adding another name (such as As-sughra (the younger) or junior) to differentiate between the girl and her mother, there is nothing wrong with that.
`Ali ibn Abi Talib (may Allah be pleased with him) named one of his daughters Fatimah, after his wife Fatimah, the daughter of our Prophet Muhammad (peace be upon him).
She (Fatimah) was not her mother; rather she was his daughter from another woman, one of the slave women of ‘Ali ibn Abi Talib (may Allah be pleased with him). So one was called Fatimah As-Sughra (the Younger) and the other was called Fatimah al-Kubra (the Elder), so as to distinguish between them. (Tahdhib at-Tahdhib, 7/136)
Almighty Allah knows best.