Divine creature in Mile End shop not revealing name (5)
I believe the answer is:
erato
'divine creature' is the definition.
(one of the muses in Greek mythology)
'mile end shop not revealing name' is the wordplay.
'end' says to take the final letters.
'shop' becomes 'rat' (I've seen this in other clues).
'not revealing name' becomes 'o' (I can't justify this - if you can you should give a lot more credence to this answer).
The last letter of 'mile' is 'e'.
'e'+'rat'+'o'='ERATO'
'in' acts as a link.
(Other definitions for erato that I've seen before include "poetical inspiration" , "Inspiring female" , "inspiration for poetry" , "Greek muse - orate (anag)" , "One of nine" .)