Unfortunately false name lacks one (4)
I believe the answer is:
alas
'unfortunately' is the definition.
('alas' is used to express regret)
'false name lacks one' is the wordplay.
'false name' becomes 'alias' (synonyms).
'lacks' suggests deleting specific letters.
'one' becomes 'I' (Roman numeral).
'alias' with 'i' removed is 'ALAS'.
(Other definitions for alas that I've seen before include "I'm sorry to say" , "What a shame!" , "Cry of regret" , "'- Poor Yorick' (Hamlet)" , "More's the pity" .)