Praise be to Allah.
There is nothing wrong with naming the daughter after her mother, if the mother’s name is a name that is mustahabb or 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 Islamic teaching, such as names that are indicative of servitude to anything other than Allah, or names that are reprehensible and off-putting.
We do not know of any shar‘i reason to disallow naming a daughter after her mother.
Shaykh Sulaymaan al-Maajid (may Allah preserve him) said:
I do not know of anything in Islamic teaching to disallow naming a daughter after her mother. Based on that, there is nothing wrong with doing that. End quote.
http://www.salmajed.com/fatwa/findnum.php?arno=17250
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 Taalib (may Allah be pleased with him) named one of his daughters Faatimah, after his wife Faatima, the daughter of our Prophet Muhammad (blessings and peace of Allah be upon him).
She (Faatimah) was not her mother; rather she was his daughter from another woman, one of the slave women of ‘Ali ibn Abi Taalib (may Allah be pleased with him). So one was called Faatimah as-Sughra (the Younger) and the other was called Faatimah al-Kubra (the Elder), so as to distinguish between them.
See Tahdheeb at-Tahdheeb (7/136)
For more information, please see the answer to question no. 217235
And Allah knows best.
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