A name in a piece of ID is a hoax (6)
I believe the answer is:
canard
'hoax' is the definition.
(I know that canard is a type of hoax)
'a name in a piece of id' is the wordplay.
'name' becomes 'n' (common abbreviation e.g. on forms).
'in' means one lot of letters goes inside another.
'a piece of id' becomes 'card' (ID card).
'a'+'n'='an'
'an' placed into 'card' is 'CANARD'.
'is a' acts as a link.
(Other definitions for canard that I've seen before include "rumour that's false" , "Unfounded rumour or story" , "A false rumour from France? (6)" , "False rumour - French duck" , "False rumour or story, from France" .)