I’ve just stumbled across this explanation of why a US state and an ex-USSR country have the same name in English.  It’s all very interesting, but it also says:

In their native tongue, Georgians refer to themselves as the Kartveli and to their country as Sakartvelo.

Which surprises me, because every Georgian man I’ve ever met has been called George, which I assumed was some sort of patriotic gesture.  But if Georgians don’t call it Georgia, perhaps they just really like the name?  I shall have to ask somebody Georgian.

Edit: I guess this might have something to do with it:

Saint George is a patron saint of Georgia. According to Georgian author Enriko Gabisashvili, Saint George is most venerated in the nation of Georgia.