Fool one in three names with chicanery, finally (5)
I believe the answer is:
ninny
'fool' is the definition.
(I know that fool can be written as ninny)
'one in three names with chicanery finally' is the wordplay.
'one' becomes 'i' (Roman numeral).
'in' is an insertion indicator.
'three names' becomes 'NNN' (an abbreviation for 'name' written three times).
'with' means one lot of letters go next to another.
'finally' indicates one should take the final letters.
The final letter of 'chicanery' is 'y'.
'i' inserted inside 'nnn' is 'ninn'.
'ninn'+'y'='NINNY'
(Other definitions for ninny that I've seen before include "dope" , "not a wise man" , "Silly billy" , "Simpleton" , "gravely so miscalled by mechanicals" .)