Decline to accept unknown boy's name (5)
I believe the answer is:
wayne
'boy's name' is the definition.
'decline to accept unknown' is the wordplay.
'decline' becomes 'wane' (wane is a kind of decline**).
'to accept' is an insertion indicator.
'unknown' becomes 'y' (algebra).
'wane' enclosing 'y' is 'WAYNE'.
(Other definitions for wayne that I've seen before include "John --, US film actor" , "Batman was Bruce -" , "- - Rooney, footballer" , "John --, film star" , "John, for example" .)