Choice ultimately mine to assume the nickname (7)
I believe the answer is:
epithet
'nickname' is the definition.
(I know that nickname can be written as epithet)
'choice ultimately mine to assume the' is the wordplay.
'ultimately' indicates one should take the final letters.
'mine' becomes 'pit' (down the pit).
'to assume' means one lot of letters goes inside another.
The final letter of 'choice' is 'e'.
'pit' going around 'the' is 'pithet'.
'e'+'pithet'='EPITHET'
(Other definitions for epithet that I've seen before include "Descriptive adjective" , "title" , "Phrase expressing some quality of a person or thing" , "Adjective expressing some quality of a person" , "Appellation" .)