Batman privately to flag in hearing (5)

I believe the answer is:

wayne

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'batman privately' is the definition.
I can't tell whether this definition defines the answer.

'flag in hearing' is the wordplay.
'flag' becomes 'wane' (I've seen this in another clue).
'in hearing' shows a homophone (sound like).
'wane' is a homophone of 'WAYNE'.

'to' acts as a link.

Can you help me to learn more?

(Other definitions for wayne that I've seen before include "John, for example" , "- - Rooney, footballer" , "John --, US film actor" , "Fort --, city in Indiana" , "John ....., later hero of western films" .)

I've seen this clue in the Sydney Morning Herald.

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