Name, popular, included by no friend (8)
I believe the answer is:
nominate
'name' is the definition.
(I know that name can be written as nominate)
'popular included by no friend' is the wordplay.
'popular' becomes 'in' ('in' can mean trendy).
'included by' is an insertion indicator.
'friend' becomes 'mate' (mate is a kind of friend).
'no'+'mate'='nomate'
'in' put within 'nomate' is 'NOMINATE'.
(Other definitions for nominate that I've seen before include "Specify (person for job)" , "give name" , "Propose for office" , "Put forward name for a mention" , "Put forward (as candidate for election)" .)