There's a different name for her (6)
I believe the answer is:
esther
'for her' is the definition.
'there's a different' is the wordplay.
'a different' indicates an anagram (letters placed in a different order).
'theres' anagrammed gives 'ESTHER'.
'name' acts as a link.
I am not very happy about this link. It may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for esther that I've seen before include "Good book" , "OT Queen of Persia" , "There's a girl from the Old Testament" , "Old Testament queen" , "Biblical heroine who became queen of Persia" .)