Famous, but not by name (5)
I believe the answer is:
noted
'famous' is the definition.
(synonyms)
'not by name' is the wordplay.
'by' says to put letters next to each other.
'name' becomes 'ed' (short for edward).
'not'+'ed'='NOTED'
'but' is the link.
(Other definitions for noted that I've seen before include "saw" , "Gaiter; oyster spawn" , "Toned down and recorded" , "Having renown" , "taken down" .)