On the first of May Elaine changes her name (7)
I believe the answer is:
melanie
'name' is the definition.
'on the first of may elaine changes' is the wordplay.
'on' means one lot of letters goes inside another (as in clothing 'on' a person).
'the first of may' becomes 'm' (1st letter of 'may').
'changes' is an anagram indicator.
'elaine' with letters rearranged gives 'elanie'.
'm' placed inside 'elanie' is 'MELANIE'.
'her' acts as a link.
This may not be right. It may be part of another bit of the clue.
Can you help me to learn more?
(Another definition for melanie that I've seen is " Girl".)