Church inscribed with Italian name (4)
I believe the answer is:
cite
'name' is the definition.
(I've seen this in other clues)
'church inscribed with italian' is the wordplay.
'church' becomes 'ce' (abbreviation for Church of England).
'inscribed with' indicates putting letters inside (I've seen this in other clues).
'italian' becomes 'it'.
'ce' enclosing 'it' is 'CITE'.
(Other definitions for cite that I've seen before include "Give as an example" , "Quote as evidence" , "Quote (a reference)" , "Quote as an example or in support" , "Quote (eg, a book)" .)