Figure "Elaine" could be her name (7)
I believe the answer is:
melanie
'name' is the definition.
'figure elaine could be' is the wordplay.
'figure' becomes 'm' (I can't explain this - if you can you should believe this answer much more).
'could be' is an anagram indicator.
'elaine' with letters rearranged gives 'elanie'.
'm'+'elanie'='MELANIE'
'her' acts as a link.
This may not be right. It may belong to another bit of the clue.
Can you help me to learn more?
(Another definition for melanie that I've seen is " Girl".)