"What is the country's name?"
As you most likely already know, Japanese does not have articles like English does. In case you really need to express something being definite, one way to do so is to use その .
My brother works at a bookstore. 私の兄は本屋で働きます I often go to see him in the/that bookstore. 私はよく、その本屋に彼を見に行きます
A) I have a country I like. B) What is the country's name? A)好きな国がある B)その国の名前は何ですか
Put more simply still, the so~ series can be used to refer to anything previously mentioned in conversation, or when you are refering to THE one. I.e., there are no other bookshops in your life. Or, no other country has been under discussion during the course of this conversation.