Writer on purpose omitting name — sorry! (8)
I believe the answer is:
penitent
'sorry' is the definition.
('penitent' can be similar in meaning to 'sorry')
'writer on purpose omitting name' is the wordplay.
'writer' becomes 'pen' (I've seen this before**).
'on' says to put letters next to each other.
'purpose' becomes 'intent' ('intent' can be a synonym of 'purpose').
'omitting' is a deletion indicator.
'name' becomes 'n' (common abbreviation e.g. on forms).
'intent' with 'n' removed is 'itent'.
'pen'+'itent'='PENITENT'
(Other definitions for penitent that I've seen before include "Regretting a wrong deed" , "Conscience-stricken" , "Regretting one's wrongdoings" , "Repentant" , "Sorry for sin" .)