Oxfordshire is a county in south-central England, in and around the Thames valley. Oxford, the university city, sits inside it, but the county is larger than the city: mainly farmland, with some old towns and pretty villages. People who live in a village twenty minutes away may still say they are “from Oxfordshire” even if they never study at the university. The name is Oxford plus -shire, an old English piece meaning a county — so it is “the shire of Oxford,” the land around that town. It is a place name on a map, not another word for the university itself, though of course the two sit together in people’s minds. Use a capital letter; it is a proper name.