Many a man's term for a pompous little girl (5)

I believe the answer is:

madam

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'term for a pompous little girl' is the definition.
I can't tell whether this definition defines the answer.

'many a man's' is the wordplay.
'many' becomes 'm' (Roman numeral for a thousand).
'a man' becomes 'adam' (Adam is an example).
'm'+'adam'='MADAM'

Can you help me to learn more?

(Other definitions for madam that I've seen before include "Formal address to a woman - precocious little girl" , "Stuck-up girl" , "Titled lady" , "What you would call a female customer (or a spoiled girl!)" , "Bossy girl" .)

I've seen this clue in the Evening Standard.

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