Remorseful writer with intent to drop first name (8)
I believe the answer is:
penitent
'remorseful' is the definition.
(similar in meaning)
'writer with intent to drop first name' is the wordplay.
'writer with' becomes 'pen' (I've seen this in other clues).
'to drop' indicates named letters should be taken away.
'first name' becomes 'n' (1st letter of 'name').
'intent' with 'n' taken out is 'itent'.
'pen'+'itent'='PENITENT'
(Other definitions for penitent that I've seen before include "Rueful" , "Sorry for sin" , "Remorseful" , "Contrite, regretful" , "Regretting a wrong deed" .)