Let it change the name (5)
I believe the answer is:
title
'name' is the definition.
(I know this)
'let it change' is the wordplay.
'change' indicates an anagram.
'let'+'it'='letit'
'letit' anagrammed gives 'TITLE'.
'the' acts as a link.
(Other definitions for title that I've seen before include "Appellation of rank" , "'The name of a book, say (5)'" , "What could be professor's" , "Rank < deed" , "Handle" .)