Supposed mean criminal gets an alias (7,4)
I believe the answer is:
assumed name
'an alias' is the definition.
('assumed name' can be a synonym of 'alias')
'supposed mean criminal' is the wordplay.
'supposed' becomes 'assumed' (synonyms).
'criminal' indicates an anagram.
'mean' anagrammed gives 'name'.
'assumed'+'name'='ASSUMED NAME'
'gets' acts as a link.
(Other definitions for assumed name that I've seen before include "I may appear under this" , "Alias" .)