My name I keep quiet: it’s no longer spoken (7)
I believe the answer is:
cornish
'it's no longer spoken' is the definition.
(ancient language)
'my name i keep quiet' is the wordplay.
'my' becomes 'cor' (both are expressions of surprise).
'name' becomes 'n' (common abbreviation e.g. on forms).
'keep quiet' becomes 'sh'.
'cor'+'n'+'i'+'sh'='CORNISH'
(Other definitions for cornish that I've seen before include "From a far SW county" , "A Celtic language" , "Rich son (anag)" , "West Country" .)