In Biblical context James would be Иаков. More common version of the name would be Яков, so a second name would be Яковлевич (male)/Яковлевна (female)

Names of the Kings and other monarchs are usually translated as opposed to common people in which case they are transliterated.
James I - Яков I, Charles I - Карл I, Henry VIII - Генрих VIII. Usual persons with that names would have been Джеймс, Чарльз and Генри.