The province has the name of the capital city , San CristÃ bal , but it was created with the name Trujillo , after the dictator Rafael Trujillo who was born in that city . San CristÃ bal is a province in the southern Dominican Republic , west of the capital Santo Domingo . It was originally named Trujillo after its founder , dictator Rafael Leonidas Trujillo , taking its present name after his assassination in 1961 .