Present and original name for Hugh, but not Cary (5)

I believe the answer is:

grant

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'present' is the definition.
(grant can mean to present or give)

I don't understand the rest of the clue.

(Other definitions for grant that I've seen before include "Formally give (a right)" , "Permit" , "... Cambridgeshire village" , "yield" , "Give (a right, property, etc)" .)

I've seen this clue in The Guardian.

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