Urge to have fashionable name (6)
I believe the answer is:
incite
'urge' is the definition.
(thesaurus)
'fashionable name' is the wordplay.
'fashionable' becomes 'in' ('in' can be similar in meaning to 'fashionable').
'name' becomes 'cite' (I've seen this in other clues**).
'in'+'cite'='INCITE'
'to have' is the link.
(Other definitions for incite that I've seen before include "Urge, instigate" , "Stir up, urge on to action" , "Move to action" , "Prompt" , "Stir up, rouse to action" .)