Silly Billy - name in case of necessity (5)
I believe the answer is:
ninny
'silly billy' is the definition.
(I've seen this before)
'name in case of necessity' is the wordplay.
'name' becomes 'n' (common abbreviation e.g. on forms).
'case of' means to remove the middle letters (like emptying a case).
'necessity' with its centre removed is 'ny'.
'n'+'in'+'ny'='NINNY'
(Other definitions for ninny that I've seen before include "Simpleton" , "gravely so miscalled by mechanicals" , "Stupid foolish person" , "Fool" , "dope" .)