Issue about name, by end of day creating antagonism (6)
I believe the answer is:
enmity
'antagonism' is the definition.
('enmity' can be a synonym of 'antagonism')
'issue about name by end of day' is the wordplay.
'issue' becomes 'emit' (I've seen this before**).
'about' is an insertion indicator.
'name' becomes 'n' (common abbreviation e.g. on forms).
'by' says to put letters next to each other.
'end of' says to take the final letters.
The final letter of 'day' is 'y'.
'emit' going around 'n' is 'enmit'.
'enmit'+'y'='ENMITY'
'creating' acts as a link.
(Other definitions for enmity that I've seen before include "Personal hostility" , "Animus" , "Antagonism, ill-will" , "Hostility between opposing people or countries" , "Hate; aversion" .)