Depends who get into power. As Fundamentalists would most likely take the power they would certainly mention it in the country's name. Something like the Islamic Republic of Arabia. Actually, it could even not mention Arabia at all since those talking about an Arab culture are mostly nationalists opposed to the religion.
However, if it would want to become more accurate it could be named "Nejd" as it's the main central territory of the country (the Sauds were formerly bedouins from the Nejd). However that would piss off Yemenites from the South and other minorities.
EDIT :
Actually I like this one.