An alternative name, not as Caliph (3)
I believe the answer is:
ali
'caliph' is the definition.
(I've seen this in another clue)
'an alternative name not as' is the wordplay.
'an alternative name' becomes 'alias' (I've seen this before).
'not' is a deletion indicator.
'alias' with 'as' removed is 'ALI'.
(Other definitions for ali that I've seen before include "Ring' specialist" , "Fourth caliph of Islam" , "Muhammad ... (former fighter)" , "Muhammad --, US boxer" , "Dickens novel" .)