Girl's name, one in a story (7)
I believe the answer is:
natalie
'girl's' is the definition.
(girl's name)
'name one in a story' is the wordplay.
'name' becomes 'n' (common abbreviation e.g. on forms).
'one' becomes 'I' (Roman numeral).
'in' is an insertion indicator.
'story' becomes 'tale' (synonyms).
'a'+'tale'='atale'
'i' put into 'atale' is 'atalie'.
'n'+'atalie'='NATALIE'
(Other definitions for natalie that I've seen before include "Wood perhaps" , "girl" , "female name" , "Girl's name" .)