Well known, though having no name! (5)
I believe the answer is:
noted
'well known' is the definition.
(I've seen this in another clue)
'having no name' is the wordplay.
'having no' becomes 'no' (I've seen this in other clues).
'name' becomes 'ted' ().
'no'+'ted'='NOTED'
'though' acts as a link.
(Other definitions for noted that I've seen before include "Famous, well-known - entered into little book" , "Illustrious" , "Remarkable" , "Significant" , "Well known; registered" .)