This country's name is that of a girl! (6)
I believe the answer is:
france
'this country's' is the definition.
(France is an example)
'name is that of a girl' is the wordplay.
I cannot really understand how this works, but
'name' could be 'fran' and 'fran' is found in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for france that I've seen before include "in E" , "[NAPOLEON] 's place" , "Land of Bordeaux and Burgundy" , "Can ref come from here?" , "Anatole ---, Fr. novelist" .)