Will written finally with name in Indian state (5)
I believe the answer is:
gonna
'will' is the definition.
('I'm gonna' means 'I will')
'written finally with name in indian state' is the wordplay.
'finally' suggests the final letters.
'with' says to put letters next to each other.
'name' becomes 'n' (common abbreviation e.g. on forms).
'in' indicates putting letters inside.
'indian state' becomes 'goa' (Goa is a state of India).
The last letter of 'written' is 'n'.
'n' put after 'n' is 'nn'.
'nn' put into 'goa' is 'GONNA'.
(Other definitions for gonna that I've seen before include "Going to (informal)" , "Shortly intending to" , "Informally, about to get" , "- - Build A Mountain (song)" .)