Assumed name I overlooked, regrettably (4)
I believe the answer is:
alas
'regrettably' is the definition.
(I've seen this before)
'assumed name i overlooked' is the wordplay.
'assumed name' becomes 'alias' (synonyms).
'overlooked' is a deletion indicator.
'alias' with 'i' taken out is 'ALAS'.
(Other definitions for alas that I've seen before include "Sadly, unfortunately" , "Exclamation of misfortune" , "express regret thus" , "Oh dear!" , "Proper, respectable" .)