Give name to capital in sheikhdom (5)
I believe the answer is:
dubai
'sheikhdom' is the definition.
(I've seen this before)
'give name to capital' is the wordplay.
'give' is a charade indicator (letters next to each other).
'name' becomes 'dub' (as in dubbing someone with a particular name).
'to capital' becomes 'AI' (resembles Ad, which can mean capital or excellent).
'dub' next to 'ai' is 'DUBAI'.
'in' is the link.
(Other definitions for dubai that I've seen before include "Gulf territory" , "sheikdom?" , "Persian Gulf state" , "Persian Gulf emirate" , "capital and port" .)