One man's name for soap (3)

I believe the answer is:

joe

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This clue might be a double definition.

'one man's' is the first definition.

'name for soap' is the second definition.
'Joe' can be an answer for 'name'. I'm unsure of the 'for soap' bit.

Can you help me to learn more?

(Other definitions for joe that I've seen before include "One of spelt out words" , "-- Orton, playwright" , "Short for Joseph" , "--- Gargery (Great Expectations)" , "-- Bloggs, ordinary man" .)

I've seen this clue in the Evening Standard.

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