Reject Percy, not very fashionable name (5)
I believe the answer is:
spurn
'reject' is the definition.
(I know that reject can be written as spurn)
'percy not very fashionable name' is the wordplay.
'percy' becomes 'Hotspur' (14th-century knight Henry Percy, nicknamed Hotspur).
'not' suggests deleting specific letters.
'very fashionable' becomes 'hot' (I've seen this in another clue).
'name' becomes 'n' (common abbreviation e.g. on forms).
'hotspur' with 'hot' removed is 'spur'.
'spur'+'n'='SPURN'
(Other definitions for spurn that I've seen before include "Contemptuously dismiss" , "Cold-shoulder" , "Reject with contempt" , "Slight" , "Repulse" .)