Greek character -- adapt it to a name for variant (8)
I believe the answer is:
mutation
'variant' is the definition.
(thesaurus)
'greek character adapt it to a name' is the wordplay.
'greek character' becomes 'mu' (letter from the Greek alphabet).
'adapt' indicates an anagram (I've seen 'adapting' mean this).
'name' becomes 'n' (common abbreviation e.g. on forms).
'it'+'to'+'a'='ittoa'
'ittoa' is an anagram of 'tatio'.
'mu'+'tatio'+'n'='MUTATION'
'for' acts as a link.
(Other definitions for mutation that I've seen before include "Genetic shift" , "Change in genetic structure" , "Change, especially biological or genetic" , "Change in genetic material" , "Natural change process" .)