A name written around my nut (5)
I believe the answer is:
acorn
'nut' is the definition.
(I've seen this in another clue)
'a name written around my' is the wordplay.
'name' becomes 'n' (common abbreviation e.g. on forms).
'written around' means one lot of letters goes inside another (some letters go around others).
'my' becomes 'cor' (both are expressions of surprise).
'a'+'n'='an'
'an' going around 'cor' is 'ACORN'.
(Other definitions for acorn that I've seen before include "Dirt on a liquid surface" , "fruit in a cup" , "Model in stone" , "From which a "tall oak" may grow" , "Potential oak" .)