On no account mention purchase of false name, son (2,2,5)
I believe the answer is:
by no means
'on no account' is the definition.
(synonyms)
'mention purchase of false name son' is the wordplay.
'mention' shows a homophone (sound like) (I've seen 'mentioned' mean this).
'purchase' becomes 'buy' (buy is a kind of purchase).
'of false' is an anagram indicator (I've seen 'false' mean this).
'buy' sounds like 'by'.
'name'+'son'='nameson'
'nameson' with letters rearranged gives 'nomeans'.
'by'+'nomeans'='BY NO MEANS'
(Other definitions for by no means that I've seen before include "Forbids" , "Certainly not, perish the thought" , "Definitely not" , "Certainly not, not in any way" , "Without using any method" .)