Girl with her own band (5)
I believe the answer is:
alice
'girl' is the definition.
(girl's nae)
'with her own band' is the wordplay.
'with' is a charade indicator (letters next to each other).
'her' becomes 'Ali'.
'own band' becomes 'ce' (I can't explain this - if you can you should give a lot more credence to this answer).
'ali'+'ce' is 'ALICE'.
Can you help me to learn more?
(Other definitions for alice that I've seen before include "Immortal girl created by Lewis Carroll" , "Girl in literary Wonderland" , "Celia (anag.)" , "Adventurous girl created by Lewis Carroll" , "Immortal girl in Wonderland" .)