Some fanciful name for part of the arm (4)
I believe the answer is:
ulna
'part of the arm' is the definition.
('ulna' is part of 'arm')
'some fanciful name for' is the wordplay.
'some' indicates a hidden word (some of the parts of the word are used).
'ULNA' is hidden within 'fanciful name for'.
(Other definitions for ulna that I've seen before include "Long bone in the arm" , "One in arms" , "Part of bone-structure" , "part of anatomy" , "One of two bones of the forearm" .)