Saudi Arabia: the Arabia of the Saud family. Also the only* country unambiguously named after its rulers. * There are a few borderline cases like Liechtenstein and the Hashemite Kingdom of Jordan though.
Philippines - King Philip II of Castille
A country named after a city in another country: Venezuela - Little Venice
A capital city named after the leader of another country: Monrovia, Liberia - after US President Monroe
A country named after it's discoverer from another country: USA - Italian Amerigo Vespucci
A country named after its liberator from another country: Bolivia - Venezuelan Simon Bolivar
A country named after another country: Indonesia - *Indian Islands*
An American state named after a fictional muslim ruler: California - from an old Spanish romance novel
about a fictional *Queen Calafia,*
derived from *Khalif(a)*
The fortunate and unexpected discovery that serendipity is named after a country: Serendip - old Arabic/Persian name for Ceylon, Sri Lanka