Delighted with name (3)
I believe the answer is:
'name' is the definition.
'delighted with' is the wordplay.
'with' says the answer is hidden in the clue.
'ELI' is hidden in the letters of 'delighted'.
(Other definitions for eli that I've seen before include "Shiloh priest (Bible)" , "Old Testament priest, the prophet Samuel's teacher" , "Man's name" , "Highest priest at Shiloh" , "Man" .)