Brothel-keeper married first man (5)

I believe the answer is:

madam

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'brothel-keeper' is the definition.
I can't tell whether this definition defines the answer.

'married first man' is the wordplay.
'married first' becomes 'm' (ast letter of 'married').
'man' becomes 'adam' (man's name).
'm'+'adam'='MADAM'

Can you help me to learn more?

(Other definitions for madam that I've seen before include "pompous young lady?" , "Leader of House of Congress" , "formidable woman" , "Courteous form of address to a woman" , "Woman of standing" .)

I've seen this clue in The Sun and The Times.

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