It's a name, but if heartless he'd be nameless! (5)
I believe the answer is:
anton
'if heartless he'd be nameless' is the definition.
The definition suggests a singular noun which matches the answer.
'it's a name' is the wordplay.
'it's a' becomes 'an'.
'name' becomes 'ton' (I am not sure about this - if you are sure you should believe this answer much more).
'an'+'ton'='ANTON'
'but' is the link.
Can you help me to learn more?
(Other definitions for anton that I've seen before include "Chekhov maybe" , "-- Bruckner, composer" , "-- Chekhov, Russian dramatist" , "Boy" , "Chekhov, say" .)