Change one's mind about name being included in lease (6)
I believe the answer is:
relent
'change one's mind' is the definition.
(I've seen this before)
'about name being included in lease' is the wordplay.
'about' becomes 're' (regarding**).
'name' becomes 'n' (common abbreviation e.g. on forms).
'being included in' is an insertion indicator.
'lease' becomes 'let' ('let' can be a synonym of 'lease').
'n' put within 'let' is 'lent'.
're'+'lent'='RELENT'
(Other definitions for relent that I've seen before include "Capitulate" , "Decide to be kind after all?" , "Be more lenient, abandon harsh intentions" , "Be merciful" , "Abandon cruel treatment" .)