Scarlet woman in court, English: her name? (9)
I believe the answer is:
charlotte
'her name?' is the definition.
(woman's name)
'scarlet woman in court english' is the wordplay.
'scarlet woman' becomes 'harlot' (both can mean a promiscuous woman).
'in' is an insertion indicator.
'court' becomes 'ct' (abbreviation used in road names).
'english' becomes 'e' (abbreviation).
'harlot' placed within 'ct' is 'charlott'.
'charlott'+'e'='CHARLOTTE'
(Other definitions for charlotte that I've seen before include "Dessert" , "Pudding; girl" , "associated with the Web?" , "US city" , "Fruit dish" .)