Change name in secret (7)

I believe the answer is:

convert

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'change' is the definition.
(I know that change can be written as convert)

'name in secret' is the wordplay.
'name' becomes 'Con'.
'in secret' becomes 'vert' (I can't justify this - if you can you should give a lot more credence to this answer).
'con'+'vert'='CONVERT'

Can you help me to learn more?

(Other definitions for convert that I've seen before include "new enthusiastic believer?" , "Change from one thing to another" , "Proselyte" , "succeed at Twickenham" , "Win over opponent" .)

I've seen this clue in The Telegraph, The Sun and The Guardian.

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