Alice's new name (5)
I believe the answer is:
celia
'name' is the definition.
'alice's new' is the wordplay.
'new' indicates an anagram.
'alice' with letters rearranged gives 'CELIA'.
(Other definitions for celia that I've seen before include "Frederick's daughter" , "lady" , "Rosalind's cousin" , "Daughter to Frederick" , "Character in Tales from Shakespeare" .)