Short piece needing correction, with name for one composer finally changed (10)

I believe the answer is:

concertino

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'short piece' is the definition.
(short piece of music)

'correction with name for one composer finally changed' is the wordplay.
I cannot really see how this works, but
'name' could be 'con' and 'con' is found in the answer.
'one' could be 'er' (I've seen this in other clues) and 'er' is present in the answer.
This may be the basis of clue (or it may be nonsense).

'needing' acts as a link.

Can you help me to learn more?

I've seen this clue in The Guardian.

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