One daughter being what makes her who she is (8)
I believe the answer is:
identity
'what makes her who she is' is the definition.
(your identity makes you who you are)
'one daughter being' is the wordplay.
'one' becomes 'I' (Roman numeral).
'daughter' becomes 'd' (genealogical abbreviation).
'being' becomes 'entity' (I've seen this in other clues).
'i'+'d'+'entity'='IDENTITY'
(Other definitions for identity that I've seen before include "equation" , "Absolute sameness; personality" , "Distinct personality of an individual" , "A person's individuality" , "Self" .)