Intended inscribes name in heart (5)
I believe the answer is:
meant
'intended' is the definition.
(to mean something is to intend it)
'name in heart' is the wordplay.
'name' becomes 'n' (common abbreviation e.g. on forms).
'in' means one lot of letters goes inside another.
'heart' becomes 'meat' (synonyms).
'n' placed within 'meat' is 'MEANT'.
'inscribes' is the link.
This may not be right. It may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for meant that I've seen before include "Deliberate" , "Aimed" , "represented" , "Had as intention or purpose" , "Intended, had in mind" .)