Deal with the matter of a name (6)

I believe the answer is:

handle

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This clue might be a double definition.

'deal with' is the first definition.
(synonyms)

'matter of a name' is the second definition.
'handle' can be an answer for 'name' (a handle is a name). I am not certain of the 'matter of a' bit.

'the' is the link.

Can you help me to learn more?

(Other definitions for handle that I've seen before include "Trade in" , "Manage - touch - hilt" , "Grip, hold" , "Knob" , "Deal with; name (colloq.)" .)

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

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