Name of organ — forget it! (2,4)
I believe the answer is:
no fear
'forget it' is the definition.
(both can be emphatic denials)
'name of organ' is the wordplay.
'name' becomes 'n' (common abbreviation e.g. on forms).
'organ' becomes 'ear' (ear is a kind of organ).
'n'+'of'+'ear'='NO FEAR'
(Other definitions for no fear that I've seen before include "Certainly not (informal)" , "Far one (anag.)" , "Definitely not (sl.)" , "what the bold show" , "What brave man displays" .)