Name dropped by fair lady in garden (3)
I believe the answer is:
eve
'lady in garden' is the definition.
(in the Garden of Eden)
'name dropped by fair' is the wordplay.
'name' becomes 'n' (common abbreviation e.g. on forms).
'dropped by' is a deletion indicator.
'fair' becomes 'even' (I've seen this before).
'even' with 'n' taken out is 'EVE'.
(Other definitions for eve that I've seen before include "See 27" , "Day before a festival" , "Lady first appearing" , "Previous day" , "comes before Jan. 1st" .)