A saintly woman can make a man's name! (5)
I believe the answer is:
steve
'make a man's name' is the definition.
The definition suggests a singular noun which matches the answer.
'a saintly woman' is the wordplay.
'a saintly' becomes 'st' (I can't justify this - if you can you should give a lot more credence to this answer).
'woman' becomes 'Eve' (Eve is an example).
'st'+'eve'='STEVE'
'can' acts as a link.
Can you help me to learn more?
(Other definitions for steve that I've seen before include "Sir - - Redgrave (oarsman)" , "-- Jobs, Apple founder" , "Chap" , "- Reich; - Biko" , "Stephen (abbrev.)" .)