Function of register announced (4)
I believe the answer is:
role
'function' is the definition.
('role' can be a synonym of 'function')
'register announced' is the wordplay.
'register' becomes 'roll' (list of names).
'announced' shows a homophone (sound like).
'roll' sounds like 'ROLE'.
'of' acts as a link.
(Other definitions for role that I've seen before include "Function; part" , "Character" , "Part in play, film etc" , "Actor's part" , "Playing part" .)