Strict name indicator (6)
I believe the answer is:
narrow
'strict' is the definition.
(narrow can mean strict or precise)
'name indicator' is the wordplay.
'name' becomes 'n' (common abbreviation e.g. on forms).
'indicator' becomes 'arrow' (I've seen this before).
'n'+'arrow'='NARROW'
(Other definitions for narrow that I've seen before include "Strict" , "lacks vision" , "With sides close together" , "Strait or thin" , "Restricted in width." .)