Give name to bird in centre of Henley (7)
I believe the answer is:
entitle
'give name to' is the definition.
(I've seen this before)
'bird in centre of henley' is the wordplay.
'bird' becomes 'tit' (I've seen this before).
'in' means one lot of letters goes inside another.
'centre of' says to take the centre.
The middle of 'henley' is 'enle'.
'tit' going within 'enle' is 'ENTITLE'.
(Other definitions for entitle that I've seen before include "Name; enable" , "Warrant" , "Give (someone) rights" , "Licence" , "Name; empower" .)